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- [00:00]
Hannah Fry
It's my object today. I brought. I'm actually going to save it. I'm going to, I'm going to save telling you what it is, but it's, it's something to do with the human body and it starts off with the straw. We'll get to it in a bit. You got, you got to, you know, you got to wait for that kind of joy.
- [00:16]
Michael Stevens
I'll wait, but as always, you come first. We've got questions you guys have submitted. Thank you for doing that, by the way. They're a blast to read. I don't know how we're going to ever cover all of them. They're all so good.
- [00:27]
Hannah Fry
They are. Here's one that's come in from Kevin. I think this one's for you, Michael. I often hear scientists complaining on documentaries about maths not working or breaking. This tends to happen when maths encounters zeros. So my question is, rather than moaning about maths not working, shouldn't scientists busy themselves making a new math that doesn't have a zero?
- [00:46]
Michael Stevens
That's what I say every day. Just let's go back to not having zero and nothing will ever break, which.
- [00:53]
Hannah Fry
Is not very long ago, actually.
- [00:55]
Michael Stevens
Foreign.
- [01:02]
Hannah Fry
This episode is brought to you by Cancer Research uk.
- [01:05]
Michael Stevens
So when most people think of naked mole rats, their unusual relationship to cancer probably isn't the first thing that comes to mind.
- [01:12]
Hannah Fry
But maybe it should be, because it is incredibly rare for them to develop cancer, which could be partly down to their unique immune system or it might be the way that their cells respond to damage.
- [01:25]
Michael Stevens
So. So scientists are studying their biology for its cancer fighting secrets. It's a reminder that discoveries can sometimes come from places you don't expect.
- [01:33]
Hannah Fry
Cancer Research UK is the world's largest charitable funder of cancer research. Thousands of scientists of doctors and nurses work across more than 20 countries to help turn discoveries in the lab into new tests, new treatments and new innovations.
- [01:48]
Michael Stevens
And the impact is clear. Over the past 50 years, the charity's pioneering work has helped double cancer survival in the uk, meaning more people living longer, better lives, free from the fear of cancer.
- [02:01]
Hannah Fry
For more information about Cancer Research uk, their research, their breakthroughs and how you can support them, visit cancerresearchuk.org restiscience this episode is brought to you by Indeed. Stop waiting around for the perfect candidate. Instead, use Indeed sponsored Jobs to find the right people with the right skills fast. It's a simple way to make sure your listing is the first candidate. C According to Indeed data, sponsored jobs.
- [02:28]
Michael Stevens
Have four times more applicants than non sponsored Jobs.
- [02:31]
Hannah Fry
So go build your dream team today with Indeed. Get a $75 sponsored job credit@ Indeed.com podcast. Terms and conditions apply.
- [02:46]
Michael Stevens
When was Xero introduced as a numeral?
- [02:51]
Hannah Fry
So it goes back to. I think it's Brahmagupta. It's in Indian mathematicians anyway. I mean they had it for a very long time. And I think that the idea is that it's about sort of the idea of a zero having that shape that circular sapiens is sort of. You're following eternity, right? So sort of the state of nothingness. But getting to Europe, it took it a really, really long time. It came through the Islamic world, really adopted it sort of came up through sp. But people were really reluctant, really reluctant to, to. To adopt it. I think Shakespeare was walking the earth before zero was, was commonly used in.
- [03:29]
Michael Stevens
Britain in like mathematics because clearly he knew about the concept of nothing. Emptiness, sure, not having any. So the reason I wanted to look at this question today was because I've got you here, Hannah, and I wanted to see how you felt too because that whole, that whole phrase, mathematics is broken, it doesn't work. We've discovered a place where if you divide by zero, math breaks. It feels so histrionic, like it's not breaking. And look, as we all enjoyed. I don't know when this is going to happen. I originally picked this question for my zero limericks, but now I did the limericks already. So that's why I was scrambling to find a different question. But division by zero or, you know, physical singularities causing science and math to break. Because you hear that all the time but it feels like clickbait.
- [04:25]
Hannah Fry
I mean generally people say math breaks when you're dividing by zero, right? Which, which I guess happens, you know, in the high school when you are just presented with it as an equation. But in, you know, much higher level mathematics and physics, there are situations where in the Navier Stokes equations, for instance, which model how fluids fl. Where you end up with what's known as singularities, where you get some denominator. I mean usually it is basically boils down to the fact that you're eventually divided by zero. You get some denominator that goes really, really small. You get a term that becomes really, really big and just blows up the whole equation. Everything else becomes. It shrinks, sort of pales in comparison to this one particular term and that the equations no longer work.
- [05:11]
Michael Stevens
So it seems like we don't need to make a new maths that doesn't have a zero. We just need to deal with zero. Better like what, what is the solution to a singularity in fluid dynamics?
- [05:24]
Hannah Fry
Uh, I mean, the, the equations break. You just can't use them anymore.
- [05:29]
Michael Stevens
They break?
- [05:29]
Hannah Fry
Yeah. I mean, they literally break. Yeah.
- [05:31]
Michael Stevens
A correspondence between the math and reality ceases to exist.
- [05:36]
Hannah Fry
Exactly. Exactly. Yeah.
- [05:38]
Michael Stevens
Okay, so what do we need to do to overcome that? Do we. I feel like getting rid of zero is the wrong answer because it's useful in a lot of other circumstances. It seems like we just need a better way of making reality correspond to it. Reality certainly isn't going, oh my gosh, there's a zero in the equation that we're all following. Time to what, create a, a rip in space time? No, the fluid keeps flowing.
- [06:07]
Hannah Fry
I think that a lot of the time when you're using equations like the ones that you find in physics for gravity, for instance, they, they tend to work really well at certain scales. So Newton's laws of gravity work really well if you and I are chucking a ball between each other. But when you zoom out further, they just, they don't quite fit as well. They sort of, they aren't powerful enough to deal with things of that scale. And likewise, when you shrink down really small, the thing that works on the scale of humans down at the quantum level, doesn't. It just doesn't work anym. So I think the thing about equations breaking, essentially that's what you're describing. You're trying to like you've got an equation that works at a certain scale, works in a certain set of assumptions, and you are like pushing the boundaries, you're right up against the very limit of what those assumptions can tell you. And that's the point when a zero gets sort of rogue zero appears. It's where exactly as you described, your description of reality departs from the real, real itself. I mean, the other place you get singularities is in black holes, right? Yeah. Obviously the physics that we know well, that you can sort of move around in doesn't apply once you get to something that's as dense as a black hole.
- [07:19]
Michael Stevens
Same with like Planck volumes and Planck distances, it's like. Well, it seems significant because physics as we have constructed it today doesn't really help us there. Or when we start trying to describe a time closer and closer to the Big Bang, we can only get so close to time zero before mathematics breaks. And I don't know why I don't like that phrase. I think it just goes back to the fact that it feels clickbaity. I think it implies that, like all of math has been Wrong the whole time. When in reality what we're just, we're, we're modeling reality really well with math. But there's some fundamental, like small scale in the universe where the universe does something different. I mean, do maybe we just need to discover zero in real life? Not emptiness, but a mathematical zero in real life?
- [08:19]
Hannah Fry
A mathematical zero in real life. What would that look like?
- [08:22]
Michael Stevens
Well, it would look like what happens in the singularity of a black hole. We don't know how reality deals with it and our equations certainly don't. But when it comes to the grade school stuff about division by zero, my opinion is that division by zero is just not division. Because one way to think of division is that it's repeated subtraction until nothing is left. But if you're subtracting zero over and over again, you're not actually subtracting. It's like saying, what's two plus tuna fish? Well, one of those isn't a number, so there's no mathematical breakage happening. You've just made a joke. But zeros that we find in our equations describing reality aren't jokes. So, Kevin, I don't think the answer is a math without zero. I think the answer is understanding real zero.
- [09:19]
Hannah Fry
Can I tell you my favourite thing about that answer?
- [09:22]
Michael Stevens
Please.
- [09:23]
Hannah Fry
The way you. I've never heard plank pronounced plonk before. I really enjoy.
- [09:28]
Michael Stevens
Is it plink?
- [09:30]
Hannah Fry
I don't know. I get this wrong all the time. Someone sent me a message the other day. We were talking about Erdos the other day and someone sent me a message saying it's Erdos. Saying it wrong. Apparently there's a. There's Euler was how I thought his name was pronounced, but apparently it's Euler. So I don't know, maybe it is plonk, but from now on I'm going to call it Plonk's Constant, because I think that sounds much cuter.
- [09:53]
Michael Stevens
It always just felt a bit more European. Plonk. Blank plank sounds like a trend from 2007. And I've, I've heard it both ways, I guess, you know, whenever I'm going to say something in a script that I've prepared, I look up how it's said and I look up what, how other people have said it. Yeah, you can't always trust the, like what Google says the pronunciation is or what YouTube videos do. I will look at like the OED or Merriam Webster and I'm like, look, if they say it's that way, then I can, I'll blame them. But Yeah, I, I, for the longest time have always said the Planck distance, but plank distance. Is that what you say?
- [10:37]
Hannah Fry
I say, I say plank. But, you know, who knows, who knows, who knows? One thing I will say is that as well as Merriam Webster, the Oxford English Dictionary, those pronunciation guides, when you work the BBC, they actually have a pronunciation unit where there's a phone number that you can call. You call up that number and you ask how to pronounce a particular. A particular word. It's especially useful when you're making science documentaries.
- [11:03]
Michael Stevens
Yeah.
- [11:03]
Hannah Fry
Anyway, one of my favorite games is to call them up and say, hello, is that the pronunciation unit? Oh, my God, they bite every single time. Anyway, there's an interesting story about what happened once. There was a very good friend of mine, Jim Al Khalili, who is a physicist, a British physicist who makes amazing documentaries in the UK for the BBC. Anyway, he was out on a shoot and there was a particular word that came up that nobody on the shoot knew how to pronounce. And he said, oh, you know what? I'm not sure. I think it might be this, but I'm not completely sure. Let's call the pronunciation unit. So they call up the pronunciation unit, they get an answer. Half an hour later, they call them back and have an answer. They record that on tape. That's what goes out on it. Anyway, the next day, Jim is in his office in Surrey University and he's still wondering about this word. So he goes next door, he goes next door to one of the physicists down the corridor and he says, oh, you don't know how to pronounce this word, do you? And his colleague says, funny you should ask. Yesterday I got a call from the pronunciation unit of the PVC and they asked me how to pronounce it. I didn't know, so I went on Wikipedia and took a guess. Look, once you get down to it, it's all duct tape. It's duct tape of WD40.
- [12:18]
Michael Stevens
You're right, it's all duct taped together and we're all just kind of feeling around in the dark. When I lived in London and I worked at Google, that was Jackpot City, because I, I sat on the floor with all the partner managers at YouTube for all of Europe, Middle east and Africa. So if I saw a name or a word say in Italian, I would just go to the Italian YouTube partner representative and I would say, how do you pronounce this? And he'd be like, basically a spaghetti of meatballs. I'm really good at Italian accents by.
- [12:54]
Hannah Fry
The way not cultural stereotyping at all. Micro.
- [12:57]
Michael Stevens
There were Germans, there were people from Iran, from Egypt. It was amazing. And it was so much more helpful than going on the Internet and trying to find what to say. All right, so let's. Let me find out what to say next. I'm going to pull out a question for you, Hannah. How about this one? This one's from Tom. What are some assumptions about the universe that scientists rely on that might someday turn out to be wrong? And what false assumption would be the most devastating to the scientific community?
- [13:28]
Hannah Fry
Okay, so, I mean, we've already one assumption that it's. That it's Planck, not Planck. That's one. That's one.
- [13:35]
Michael Stevens
And I'm devastated that we don't know.
- [13:38]
Hannah Fry
Okay. I mean, there's a few of them. There's a few of them. I'm going to go a bit bigger than the universe. I'm going to go for science in general. I think that there are lots of situations where people have theories that then end up forming the basis of. I mean, the central basis of a lot of people's careers. Right. So dark matter is one example of this where when you make a calculation about how much gravity there should be to hold the galaxy together, there's sort of. There's loads of stuff missing. This. This matter that you can't see, hence dark matter. And so it sort of. It began to really fill a hole in an equation. And now there are people who spend their entire careers studying, analyzing, trying to decipher what dark matter is. No one's ever found it, but, I mean, there is sort of quite good evidence that something like that exists. But there is this rival theory that says, well, what if Einstein was just wrong? What if we were talking about scales earlier? What if Einstein works at the scale of the solar system, but doesn't work at the scale of the galaxy? What if there is something else that's missing? So there are some other people who are working on this rival theory, which is called modified Newtonian dynamics, that says actually kick Einstein out. The whole phrase of, oh, what are you. Einstein's not going to work anymore because they're just going to disprove everything that he ever came up with. I mean, that's one really big fundamental thing that would be pretty devastating to the entire scientific community.
- [15:11]
Michael Stevens
But I hope that they can get past that devastation because that's the only way you make progress. I mean, how exciting of an idea. I've never heard of this before. Modified Newtonian dynamics.
- [15:21]
Hannah Fry
Yeah.
- [15:21]
Michael Stevens
So the idea is that Einstein is once again just an approximation. That's not good for big stuff. It's good for medium sized stuff. And then we've got the quantum realm on one side and the galactic transgalactic world on the other. Interesting.
- [15:36]
Hannah Fry
Yeah, because you, we already know that Einstein isn't a complete picture exactly as you described. Right. It doesn't, it doesn't capture things down at the small scale. So who's to say there's not another big scale above it?
- [15:47]
Michael Stevens
I always assumed, look, we've got the top half figured out. It's the, it's the bottom half that, that we still need to marry to the big. And yet maybe we're still just eating the filling of the sandwich and we don't know what two slices of bread are doing.
- [16:00]
Hannah Fry
Where is the bread, Michael? That's, that's the question. I mean, there's other things like, okay, so at our scale we make, and actually the scale of sort of galaxies and solar systems, we really make the assumption that time goes forwards, only you can't like smash a glass in reverse. Right? That's sort of this unwritten rule. But the thing is, is that at the quantum realm, I think that they're slightly less comfortable with that as a, as a baseline assumption. I mean, why should that be? And that I think is one that would really tear apart. There's also all the constants, you know, like Planck's constant.
- [16:37]
Michael Stevens
You know, I've heard of that before. I've said that before.
- [16:42]
Hannah Fry
There's other constants about, for example, the way that electrons orbit an atom and the sort of strength of those, of those forces. Who's to say that those constants have been constant throughout the entire history of the universe? Right. Maybe actually they're just. We're seeing one snapshot in time of the way that they look or one corner of the universe in which they look and look that way. All of these are fundamental assumptions that actually, you know, you still have to question. Right? Like, you can't, you can't just accept them as fact and move on. And, and I think that everything would fall apart there. But I think actually the reason why I wanted to go beyond just the universe on this was that I had one thought. There's this really brilliant piece in the Sunday Times that was about scientific publishing. And I think that this assumption that actually scientists rely on a lot is that the peer review process is great. That the way that scientists publish papers means that we end up with facts. Right. And sometimes that looks on slightly shaky ground.
- [17:48]
Michael Stevens
Right.
- [17:49]
Hannah Fry
I think that's been an assumption for a long time that scientific papers have been through such a rigorous process of peer review of other scientists, checking the numbers, checking that they work. You can trust every single scientific paper. And I think that there are a few little cracks in that. There's a few. There's quite a lot of duct tape down there as well, a lot of scientific retractions. Because the system isn't necessarily built for true stuff to come to the top.
- [18:20]
Michael Stevens
You know, new stuff, too, has a big barrier because again, it's not God reviewed, it's peer reviewed. It's other people who have their own community expectations and, and paradigms that are shared.
- [18:37]
Hannah Fry
Here's the thing, right? If you're a scientist, of course you're contributing to this great big body of knowledge. Of course you're advancing human understanding of the universe, of course you are. But you're also trying to get a job. You're also like, you know, trying to get a research grant. And the thing is, is that to do this, the things that are, you know, fundamentally and understandably selfish, sometimes they run counter to the things that serve that wide range. You know, you need to publish papers, you need to, like, get a reputation, you need to be noticed internationally, you need to, like, have people cite your work. And all of that is, you know, you do best in that situation when you are, like, pumping out papers, when you've got amazing data, when you're, like, coming up with incredible results. And so there are basically incentives in the system for people to just like, you know, fudge a little bit around the corners, like just sort of like maybe just tweak the data a tiny bit here and there, maybe publish the most interesting results that they're getting and not the boring ones.
- [19:45]
Michael Stevens
Right?
- [19:46]
Hannah Fry
And I'm not talking about necessarily direct manipulative behavior always here. I think sometimes it's sort of overlooking there's like confirmation bias, all of that kind of stuff. And the thing about the peer review system is that you're handing these papers that you're writing and you're handing them to volunteer scientists who've got their own stuff going on, who maybe don't have time or the expertise to go through and recheck every single number and, like, quite a lot of stuff slips through. So this article in the Times was, was really talking about the number of retractions that have happened in the scientific literature is increasing. And I think that with AI contributing to this landscape of like, just, you know, making it a tiny bit easier to make your paper sound amazing, just making It a tiny bit easier to like, you know, play with your data in a particular way.
- [20:33]
Michael Stevens
Right.
- [20:34]
Hannah Fry
The number of retractions is increasing because.
- [20:36]
Michael Stevens
AI as a, as like an LLM specifically is going to be able to write things that sound right. And this is what peer reviewed papers tend to sound like. And so here's one. And it passes peer reviewed review because it's been engineered by an algorithm to sound like it should. And we don't wind up making any progress. We certainly don't do anything novel or revolutionary. I also wanted to say that I think we might discover that there are limits to what we can know that we don't currently know about. I, I think it, we could prove in some like Godelian mathematical way, for example, that we will never know what consciousness is and whether one thing is conscious or not. That might actually be for some really clever reason beyond the ability of a fellow conscious being. And we're just going to be left in the dark, having to accept it on faith. And I think that I could see a far future where science is more about making people feel okay with what we cannot know. And it kind of takes the place of religion.
- [21:39]
Hannah Fry
You're such an optimist. I mean, I, I definitely agree with you about the limits of human knowledge and about accepting the limits. I don't think we're there yet, though. I do not think we're there yet.
- [21:50]
Michael Stevens
No.
- [21:51]
Hannah Fry
All right, here's one for you, Michael. I know you're gonna like this one.
- [21:54]
Michael Stevens
Okay.
- [21:54]
Hannah Fry
This is from, from Jacob. When hanging a post from my office, why do I feel compelled to hang it at the centre? I could hang it anywhere. But why does it look best if equally between two endpoints? Is there an evolutionary reason for this? I've attached a photo of it hanging in my dingy office.
- [22:11]
Michael Stevens
Okay, let's show that photo and then let's judge whether it's centered enough.
- [22:15]
Hannah Fry
Let me tell you what we're looking at here. So we've got this. It looks like one of those. It's been taken inside one of those sort of temporary buildings that you get on, on construction sites. That's sort of what it looks like. It's got a, it's a corner of a room. It's got sort of cream paneled walls. It has a window to one side. And then symmetrically between one of the wall panels hangs a glass framed photograph of a man with a guitar and a cowboy hat. Looks a bit like Bruce Springsteen from afar.
- [22:50]
Michael Stevens
First of all, I love that Jacob submitted a photo with his question as though we would read his question and go, what do you mean centering a poster? I've never seen such a thing. I need a visual here. Oh, a poster. Now I know what you're talking about.
- [23:07]
Hannah Fry
Thank you for that picture, Jacob. I mean, I would say that aesthetically there's a bit of headroom there to go, isn't there?
- [23:15]
Michael Stevens
Look, we don't need to judge Jacob's decoration, okay? He's asking about a psychological evolutionary phenomenon.
- [23:25]
Hannah Fry
Yeah, I don't think. I don't remember coming across Bruce Springsteen posters in the, the History of Evolution, but maybe I missed that lecture.
- [23:34]
Michael Stevens
Regardless of who it is, I think this is a really important question because I think it gets at like one of those, like, what is a human kind of things and why are we still here? Why did we not go extinct? I think that we really enjoy stuff that's difficult, stuff that is unnatural. I think we are a, a high skill based species where we don't hunt with the claws we're all born with. We have to like come up with strategies to hunt. And the only food sources available to these like little hairless naked apes that had no protection was the high skill stuff like let's get, let's get a mastodon or let's hunt an elephant. And that's going to require traps and cooperation and tools and spears and things that other animals just couldn't put together. And so humans that enjoyed things like, hey, look, this is symmetric or this is centered, did better when it came to surviving with such soft, fleshy bodies. So now we, we are their children, right? We also really enjoy when things are unnecessarily rule following, when they're centered, when they're symmetric. And this has been our story forever. One of my favorite mysteries is why so many ancient stone axes are symmetric when they didn't need to be. It's been shown that making these, you know, what do you call it when you nap stone to make a sharp point, making it symmetric or bifaced or, or, or giving it the shape that they seemingly all have took a lot more time than necessary to do the job of killing an animal or, or ripping the skin off the bone or the meat off the bone. And so the only explanation seems to be that we just thought it was cool looking, that it showed a level of skill that meant that we were good potential mates, that we were going to be good at other things that humans needed to be good at, like cooperation, planning, thinking ahead, imagining. So yeah, we want our posters to be centered because if we didn't we would have gone extinct.
- [25:55]
Hannah Fry
It's like I often think about the number of right angles there are in our lives.
- [26:01]
Michael Stevens
Yeah.
- [26:01]
Hannah Fry
Because nature does not have right angles. Then you don't find them. I mean, maybe very occasionally as a fluke, but in every room, in every building you ever walk into, in every object that you own, in every space that you encounter, we are surrounded by them. Surrounded by this thing that is the most unnatural of the human inventions. And I totally agree with you. It's like, why are we so obsessed with right angles? It's because they're symmetrical. You know, it's because they're neat. It's because they're sort of. There's this precision to them that we are completely drawn to. I totally agree with.
- [26:34]
Michael Stevens
That's right. There's an unnatural precision that shows a mastery of something that requires more skills than any other animal would require, and that's us. The only way we could survive was by having that high skill.
- [26:50]
Hannah Fry
So there you go. Actually, I started off by slagging off your Bruce Springsteen poster, But actually, now. Now you've got the. You know, the line of your window, You've got the really sad foam panels in the ceiling. You got right angles and symmetry all over the place. Jacob, you are demonstrating yourself as uniquely human.
- [27:10]
Michael Stevens
I'm trying to make this picture bigger. Ah, okay. So it's not Bruce Springsteen. It's a guy in a cowboy hat.
- [27:17]
Hannah Fry
Maybe it's Jacob himself.
- [27:18]
Michael Stevens
Oh, wouldn't that be cool? And we're sitting here not admiring it enough.
- [27:23]
Hannah Fry
Oh, hold on a second. Now that we've zoomed in, it's not Bruce Springsteen at all. It's Clint Black. Okay. This is a signed poster. Actually, he says it in his email. A signed poster from 1990. I don't know who Clint Black is, but I know what he looks like now, thanks to this image. I think at that point, maybe we'll go to a break, shall we?
- [27:48]
Michael Stevens
This episode is brought to you by Cancer Research UK, who over the past 50 years, have helped double cancer survival in the UK.
- [27:56]
Hannah Fry
You might have heard of BRCA genes. These are the ones that made headlines when Angelina Jolie revealed that she carried a faulty version.
- [28:03]
Michael Stevens
Yeah. BRCA genes are part of our DNA. They help to repair cells and keep them healthy. The risk comes when BRCA genes are faulty, and about 1 in 400 people inherit a faulty version, increasing the risk of some cancers.
- [28:16]
Hannah Fry
Yeah. Now, this discovery came From Cancer Research UK scientists who came across the BRCA1 and BRCA2 genes. A breakthrough that changed how doctors prevent diagnose and treat cancer. And now we've got genetic testing that means that people who have faulty BRCA genes can take steps to prevent cancer or to receive tailored treatment.
- [28:36]
Michael Stevens
Yeah. The discovery also revealed a weakness in cancer. By turning that flaw against the disease, researchers developed PARP inhibitors, targeted drugs that are now helping thousands of people.
- [28:47]
Hannah Fry
And all of this really points to a future where medicine is no longer just one size fits all. It's something that's, that's informed by your own DNA. So for more information about Cancer Research uk, their research breakthroughs and how you can support them, visit cancerresearchuk.org restiscience this.
- [29:05]
Michael Stevens
Time of year, everyone talks about going dry. But at Athletic Brewing Co. We're skipping that because we prefer going athletic, which isn't dry at all. From crisp goldens to hoppy IPAs and limited releases, in between, you'll find something that fits your style. Every single non alcoholic brew is packed with flavor and the same craft experience, experience you love. So, yeah, you could call it dry, but there's really nothing dry about it. Find your new favorite near beer@athleticalbrewing.com Athletic Brewing Co.
- [29:33]
Hannah Fry
Fit for all times. All right, we're back. And this time I've got another question for you, Michael. How many. How many holes does a straw have?
- [29:48]
Michael Stevens
One.
- [29:50]
Hannah Fry
Are you sure?
- [29:51]
Michael Stevens
Yeah, I'm sure. I mean, if we're talking about topological holes, holes that cannot be removed by gluing or ripping one, this is a.
- [29:59]
Hannah Fry
Topic of much debate on the Internet. You know, of how many holes does a straw have? Because as you say, some people say one, it's just, you know, you look through it, it's a hole done. Other people say that there's two because there's one on this end and there's one on the other end. And in many ways both. Both groups of people, I think, have a point. Sort of.
- [30:20]
Michael Stevens
They have a point. I mean, you know, I did a video on how many holes a human has. And I think the bottom line is that here's what a hole is. It's a word. We made it up and it can mean whatever we want. And most of these debates are around what the word should mean. Should it mean like an individual entrance or is there some better definition? So look, by using a mathematical definition of a hole, the straw has one. You can imagine taking one end of the straw and stretching it open so that you wind up with a plate with a hole in the middle. Then it's really obvious that you've got one hole.
- [30:55]
Hannah Fry
I mean, of course you are absolutely right. I. I'm gonna come to your video on the. On how many holes a human has in a moment, if I may.
- [31:03]
Michael Stevens
I'm really curious about what object you've brought because we're jumping right into holes. Oh, yeah. Which we've established. Matters a lot to me.
- [31:10]
Hannah Fry
It does, evidently. Okay. But really what I want to talk about here is topology, which is. It's basically the Alice in Wonderland of mathematical ideas. It's where. It's where you take a shape, and the rules are that you can bend it and stretch it and deform it as much as you like, but you cannot cut it. Right? You cannot cut it, you cannot rip it, you cannot crease it. And then people have these arguments extensively about how many holes things like straws or T shirts or trousers have. Now, okay, while I agree with you that fundamentally, I think that a straw has one hole, you could say, well, hold on a second. If I cover up one end here, if I pinch one end of the straw now, how many holes does it have? Because it's sort of. You could say that it sort of does. Still. Does still have a hole. There's sort of a hole on the end. No.
- [32:00]
Michael Stevens
Right. Okay. So, I mean, I would say that first of all, you have pinched a hole shut. All right? So you, You. You have. You're no longer talking about topology because you've committed a heteromorphism. It's now a different shape. You have glued one in shut, and you don't have a hole anymore. You have a blind hole, which is a hole that you cannot go all the way through. But those can be removed by just, you know, moving the thing around like clay.
- [32:26]
Hannah Fry
Okay, sure. But then, hold on a second. What about this glass? Does this glass have a hole in it?
- [32:31]
Michael Stevens
No.
- [32:32]
Hannah Fry
Why not? What are you talking about? It's got a hole right there.
- [32:34]
Michael Stevens
Yeah, but I can get rid of that hole without needing to use any glue or scissors. I can just. If we imagine that the glass is made of clay, I can open its orifice larger and larger until the whole thing is flat and it's a plate.
- [32:45]
Hannah Fry
Okay? So this is, I think, the fundamental key point. The two ways that you can look at this straw. One is that you can say that the surface is two dimensional, that the paper around the outside is 2D, and you can imagine blowing up this straw until it's the size of a balloon. Okay? So it's like this big, round balloon.
- [33:04]
Michael Stevens
Oh.
- [33:05]
Hannah Fry
At which point then there are these two circles that are cut into it. Those are boundaries, right? So I think that exactly as you pointed out at the beginning, the problem is that the word hole means two different things. Sometimes it means tunnel and sometimes it means a boundary. So you could say that this straw, if it was the shape of a balloon blown up to the shape of a balloon, would have two circles cut in it. Two boundaries, essentially. And so that is like the argument in favor of the people who say that a straw has two holes, one, one at each end.
- [33:38]
Michael Stevens
What field of mathematics worries about holes as boundaries? Because I do, I do appreciate the difference between these two conceptions. A topologist would, would, would say this shape still has just one hole.
- [33:53]
Hannah Fry
I think it's still a topologist. It's just, it's. The topologist is on looking at the surface rather than the, the a three dimensional object.
- [33:59]
Michael Stevens
No, I'm not sure. I think you're right.
- [34:02]
Hannah Fry
I don't, I don't know if a definition, I would say topologist, but maybe I'm, maybe I'm wrong. The other way to look at this straw is to say, okay, well, imagine it was made of plasticine, at which point you could. Well, you could also cut off a tiny bit of it, make it shorter and shorter and shorter and shorter and shorter until you had just a little ring that was left over. At which point you're like, that's definitely got one hole. I mean, you're kind of crazy to imagine anything else. It's the same shape as a donut. A donut obviously has one hole, right? So those are the two different ways to look at it, right? As though the surface is paper, two dimensional or the surfaces are sort of physical object itself. A three dimensional object itself.
- [34:42]
Michael Stevens
If we blow the straw up to a balloon. I like this way of thinking about it. Because now we've got seemingly two boundaries though a topologist would say, but I could put my fingers into one of those boundaries and pull it and stretch the balloon until it was just a circle with a hole in the middle. One hole, right?
- [35:01]
Hannah Fry
So this is exactly it, right? Is that it's like you've got two boundaries on the surface, but if you consider that the whole object is like solid, then it's one tunnel. So there's a difference between boundaries and tunnels, which is where the confusion comes in. So, okay, it's all right. It's not so bad on a straw. But what about a T shirt? How many holes does a T shirt have?
- [35:22]
Michael Stevens
Well, it has three holes, right? It's got four openings, the head hole and the torso hole. Top and bottom are like one hole, but then it's got two more openings that join the central cavity of that hole, the armholes. So you can imagine shuffling them around and creating three very distinct through holes in a T shirt.
- [35:45]
Hannah Fry
I really think the blowing it up into the balloon thing is really helpful here, because if you imagine taking a T shirt and blowing up into a balloon, then you've got four circles cut on the balloon. That's right, Exactly. But you're right that if it was. If the T shirt itself is, like, made of plasticine, then essentially you have one tunnel, one central tunnel from top to bottom, and then two additional tunnels that join that tunnel. So three holes in total. Okay. So mathematicians love playing around with these ideas of, like, taking really kind of crazy, intricate shapes, manipulating them, asking whether a sphere can pass through itself, asking whether you can, like, invert a donut, all of these kind of things. But the reason why this is fun and the reason why this matters, I think, is because of what happened with early life in the universe because it was basically playing this topological game. So the earliest, earliest organisms, they tried to digest food in a sort of. As. As though they're a sack, right? So sort of imagine, you know, jellyfish here or anemones, okay? So they're. They're. They eat with the same hole that kind of goes into their stomach. They digest it and then they sort of basically spit this waste out the same hole, which is inefficient. Pooping and eating out of the same hole is not a good idea, I would say.
- [37:04]
Michael Stevens
Yeah, don't. I don't need to be told that.
- [37:09]
Hannah Fry
And then around about 550 million years ago, right, Like, I mean, quite a long time ago, there was this worm like creature that did the. I mean, it was the first one that did this really incredibly revolutionary thing. It essentially evolved a second hole, second boundary, but in effect, made the hole into a tunnel. So it stopped being like a poke into the. Into the body of the creature and actually became a tunnel, a tunnel all the way through.
- [37:39]
Michael Stevens
So this creature, how long ago did it emerge?
- [37:42]
Hannah Fry
550 million years ago.
- [37:44]
Michael Stevens
That doesn't seem that long ago, to be honest. For the first butthole. For the first living donut.
- [37:51]
Hannah Fry
The first butthole.
- [37:52]
Michael Stevens
That's great. That's cool.
- [37:56]
Hannah Fry
The first butthole. Michael, I love working with you. You're so right. That is the evolution of the butthole. Is that what we call this video?
- [38:03]
Michael Stevens
We haven't even been around for a billion years.
- [38:07]
Hannah Fry
Anyway, the butthole as an innovation was genius. Okay? So so much of life on the planet. I mean, basically every creature that you can imagine that, that eats at one end and then ejects waste at the other is like following this moment of revolution. And this is the thing now you can eat continuously, right. You've got, what you've done is you've, you've turned yourself topologically into a different shape and now you can have this like assembly line of food. And that is what allowed animals to get way bigger and way more complex.
- [38:43]
Michael Stevens
It's a miracle. That's why I think eating on the toilet is almost a religious experience. It's a celebration of the fundamental donutness of my body.
- [38:53]
Hannah Fry
Yeah, right. Because we are, we are like squish us down, we are all these donut shapes. Yeah. It's also though, the reason why our brains and our eyes and our nose and our mouth are all in the same place. Cause think of us as though we are just a tube that's existing through the world that's like continually looking for food. Sort of imagine us worm shaped, right. And we have all of our senses packed up towards the like, entrance to our fundamental tube.
- [39:24]
Michael Stevens
Yeah, that's right.
- [39:25]
Hannah Fry
It creates a bit of a problem though, because you need the tube, the kind of the esophagus to go through the middle. Right. You want the brain to kind of exist all the way around the tube. You don't want the brain on one side and nothing on the other. So there are some very simple animals, even anthropods, I think, where the esophagus literally goes through the middle of their brain. So if they swallow a chunk of food that is too big, they can give themselves brain damage, which is not great.
- [39:54]
Michael Stevens
I'm glad that's not us.
- [39:56]
Hannah Fry
Do you know how humans worked out our way around it? Well, not humans, but I mean mammals more generally.
- [40:00]
Michael Stevens
No, no.
- [40:01]
Hannah Fry
How so? If you think we have like kind of you're eating through your mouth, you have your breathing through your nose, which is above, above your mouth. But then once it gets to your throat, they have to swap over. You have to go to your lungs.
- [40:18]
Michael Stevens
The nose goes into the sinuses.
- [40:20]
Hannah Fry
Yeah.
- [40:21]
Michael Stevens
And they all connect in the throat, the mouth hole and the nose hole. But then there is a division between the esophagus and the trachea for air and food. And for humans that's a dangerous connection. It's much easier for us to choke than like a dog or a bear.
- [40:44]
Hannah Fry
I thought I understood this and now I'm thinking about it. I'm not sure I completely do this little bit. Oh, there we Go look at this.
- [40:50]
Michael Stevens
Yeah. So here you can see the mouth opens up and comes down this way into the throat. But the nose goes into this big open area called the sinuses. And this connects back into throat to the throat as well. They come down, and then here we have this division between the esophagus and the trachea. So air that we breathe comes down here to the lungs, and food is squeezed by the muscles in the esophagus to get to the stomach.
- [41:20]
Hannah Fry
So here's the problem, is that you need the stomach to go in the middle of the body, right? But at the nose, it's like the airway is on top. It's sort of. It's kind of at the back, as it were. And then they switch over. They cross over in that section where the air supply starts to come to the front. Right? So originally it's at the back, and now it comes to the front. You've got this crossover, the switchover. And it's the topological solution to the fact that we need our brains to be around our whole body. You need the tube to be in the center. And how do you sort of. How'd you do it?
- [41:54]
Michael Stevens
Yeah.
- [41:55]
Hannah Fry
You with me?
- [41:56]
Michael Stevens
I'm with you. And it makes me appreciate the existential quality of choking, that it's fundamentally because of this crossover that has to happen.
- [42:05]
Hannah Fry
The crossover has to happen. Exactly. The brain's on top, the nerve cord is on the bottom. You've got to have your connecting nerves physically to wrap around the esophagus to link up so the brain can act around the entire body. And so what you end up with is this, like, switch over. All right? So we're all these tubes munching along, eyes and ears and stuff, all at the top. But then we also, of course, have breathing apparatus attached. Right? Our noses. Now, I know that you have done a video on this. Tell me, how many holes are there in the human body in topological terms?
- [42:44]
Michael Stevens
Okay, to make it brief, I'll say that we need to define how big something has to be to be a hole. Like, if a single blood cell can pass through it, then the body has millions of holes, right? The urethra is a hole because you can get up into the bladder through the ureters to the kidneys, blah, blah, blah, blah, blah. So I think we need to go bigger than that. If we go 60 microns, all right, the thickness of a human hair, if it can come in one hole and come out another, we've got ourselves a through hole. And as it turns out, humans have Eight entrances, meaning we have seven topological holes.
- [43:19]
Hannah Fry
Seven topological holes. Ears don't count, paws don't count. Female reproductive organs don't count.
- [43:25]
Michael Stevens
That's right, the ears don't count because the eardrum blocks any continuous passage from the ear into anything else. At the scale of a, of a, a human hair. Right. A neutrino can pass right through the eardrum. A neutrino can pass right through reproductive organs and go wherever it wants. But a little spaceship 60 microns wide, it's going to be like, guys, we're stuck. We've got eight ways in and out and that means we've got seven holes.
- [43:54]
Hannah Fry
There was a program that I was doing a few years ago about evolution and we were talking about how all creatures were tubes. And I mentioned the fact that you had done this seven holed human thing and was extremely excited about it and just absolutely loved it. And so I also, by the way, at the time was quite obsessed with woodturning videos on the Internet, which I'd also mentioned on the show. Anyway, someone made me wood turned me a topological model of a human body.
- [44:26]
Michael Stevens
Oh, it's beautiful.
- [44:28]
Hannah Fry
Isn't that gorgeous?
- [44:29]
Michael Stevens
You know, it looks like the cylinder of a revolver.
- [44:35]
Hannah Fry
That's right.
- [44:36]
Michael Stevens
There's a central hole that it could pivot around and then there are six holes for the six bullets. And that's the human body. Topologically that's the same thing. We haven't discussed what these other six holes are like. We know that there's this hole from the mouth to the anus, but there are six more tunnels that all join in to that same tube. Two of them are the nostrils. You've got your left and your right nostril. They meet together in the sinuses and then they connect up with the throat. And then you have, on both eyes you have two holes that are called your lacrimal punctum. And they absorb your tears. If you're actually crying, they can't keep up. And so the tears come down on your face. But normally the wetness of your eyes is, it's like squirted on the eye and then it drains through these two holes we have at the corners of our eyes. And that goes into the sinuses as.
- [45:29]
Hannah Fry
Well, to the back of your throat.
- [45:31]
Michael Stevens
That's why when you get really teary, your nose runs. A lot of that crying nose running liquid is actually tears that are in your nose now, now. So you've got those four puncta, two in each eye, two nostrils, that's the six holes that all join up and they are greater than 60 microns across. So they fit my definition of a hole that, you know, you could travel through, you can stick a hair through and pull it out somewhere else. So that's all seven of them. You've got the.
- [45:57]
Hannah Fry
Hey, mouth to bum right here in the middle.
- [45:59]
Michael Stevens
It's the middle one, let's say. Yeah. And then you've got the two nostrils.
- [46:03]
Hannah Fry
Nostril, nostril, right there.
- [46:04]
Michael Stevens
And then you've got the four lacrimal.
- [46:07]
Hannah Fry
Puncta, Left eye, right eye, human.
- [46:10]
Michael Stevens
Yep. And they all connect. But you can. And this is hard to do if you're just listening, but you can imagine all of those tunnels being morphed and continuously deformed away from each other to form exactly the shape Hannah is holding. That's us.
- [46:28]
Hannah Fry
That's us right there. Just. Just that. Really loving right angles as well. This is us. Us and right this and right angles. That's the whole description of humanity that you ever need. You know what? Forget about the Arecibo message. This is what we should have sent.
- [46:42]
Michael Stevens
Yeah, they would have gotten it. Like, in general, this is us.
- [46:45]
Hannah Fry
I mean, it'd be better than the other one they sent, frankly.
- [46:48]
Michael Stevens
We could have sent a. A board of wood with two holes drilled in it and said, this is our pants drill. A third hole. It's a shirt.
- [46:58]
Hannah Fry
Yeah, yeah. Unless. Unless it's a button up shirt, in which case the first one would do.
- [47:03]
Michael Stevens
Ooh, yes, yes. And by the way, like, we all in general have seven holes, but if you've got piercings, those add additional holes.
- [47:15]
Hannah Fry
Oh, gosh. Oh, they do. You're absolutely right. I need to put in a teeny tiny. Especially a nose piercing. I need to put in a teeny tiny one in there.
- [47:24]
Michael Stevens
And not to get too into the weeds, but some people have additional holes through their sinuses. I forget what the medical term is for it, but we don't really know if we have them unless we've had like, scans or like nasal problems. But you can live your whole life not knowing that you've got an eighth hole hidden inside your head.
- [47:43]
Hannah Fry
Or someone with two buttholes.
- [47:45]
Michael Stevens
There aren't many of them, but I've met some people that I've been suspicious. I'm like, you've got two down there, don't you?
- [47:53]
Hannah Fry
You're talking out of your second butthole.
- [47:56]
Michael Stevens
Yeah. It requires a whole different language. But it's possible now that we've done.
- [48:00]
Hannah Fry
An evolutionary history of the butthole, I think. I think we put this episode to bed, Michael. That was. That was an enjoyable, an enjoyable romp.
- [48:08]
Michael Stevens
Let's flush all of it. All right, guys, thanks for joining us. I'm glad you've got your seven plus holes and we hope you bring them back next time.
- [48:19]
Hannah Fry
Certainly do. If you have any questions you'd like us to answer, anything you want to send us in, you can send us anything you like.
- [48:26]
Michael Stevens
Thereestiscienceolehanger.com and you can join our newsletter@therealestis.com.
- [48:33]
Hannah Fry
Science we're going to be back next Thursday with another edition of Field Notes and on Tuesday with our usual normal episode where we will not be talking about buttholes. Stay there.
- [48:43]
Michael Stevens
Probably not, but until then, stay curious.
- [48:51]
Hannah Fry
Sam.