Michael Wrote Some Math Poetry

Summary

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The Rest Is Science – “Michael Wrote Some Math Poetry”

Podcast: The Rest Is Science
Hosts: Prof. Hannah Fry, Michael Stevens (Vsauce)
Release Date: February 5, 2026

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Episode Overview

This episode explores how scientific and mathematical ideas—often taken for granted or assumed to be fully understood—can become strikingly strange when seriously questioned. The hosts tackle deep philosophical questions about the nature and correctness of mathematics, the acceptance of scientific ideas like germ theory, and the peculiar dynamics of hurricanes in fluid mechanics. The episode then segues delightfully into the unlikely territory of mathematical poetry, with Michael sharing and composing limericks that blend mathematical rigor with playfulness.

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Key Discussion Points & Insights

1. Show and Tell: Museum of the Mind

[02:15–02:53]

• Michael introduces the “Fieldnotes” episodes as an interactive show and tell, inviting audience contributions.
• The episode’s theme: “the fusion of math and poetry.”
• The first listener question is chosen: “How do we know math is correct?” from Noor.

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2. How Do We Know Math Is Correct?

[03:02–13:30]

• Big Question: Is mathematics a human invention or a discovery about the universe?
• Hannah Fry (on the uncertainty of mathematical truth) [03:25–04:22]:

  “We are in a position where maths is either this, like, massive hallucination that all of us have come up with that just so happens to work perfectly, or it really is the language of the universe.”

• Michael Stevens references Wigner’s famous essay on “The Unreasonable Effectiveness of Mathematics.” [04:22–04:29]
• Real-World Examples: Antimatter, Neptune’s prediction—mathematical equations predicting unknown phenomena in reality. [04:36–05:58]
• Correctness Defined: The hosts discuss the difference between correctness (philosophical truth) and effectiveness (correspondence to reality).
• Foundations of Math:
  • Attempts in the early 20th century (e.g., Principia Mathematica by Russell & Whitehead) to prove math’s consistency and correctness.
  • Gödel’s Incompleteness Theorem: The limits to proving math’s foundations. [07:26–09:09]
• Memorable Exchange:
  • Michael: “Sometimes you just have to embrace the religious aspect of math, which is that through faith alone, I accept that one plus one equals two. Now let’s move on.” [09:49]
  • Hannah: “When it comes down to it... it’s all an act of faith.” [10:03]

Invented or Discovered?

[10:54–13:30]

• Hannah’s Conclusion:
  • Tools and notation are invented.
  • The phenomena revealed by math are discovered.
  • Cites Andrew Wiles’ metaphor: doing research math feels like stumbling through a dark hedge, suddenly realizing it's a “perfectly manicured garden.”
  • Quote:

    “[You] are in absolutely no doubt whatsoever that it is not of your invention, that you are exploring a space that exists beyond the human mind.” [12:00–13:03]

• The philosophical question is left open for further discussion if listeners wish.

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3. Why Was It Hard to Accept Germ Theory? (The Semmelweis Reflex)

[13:56–19:54]

• Listener Question: How difficult was it for the discoverers of germs to convince others of their existence?
• Semmelweis Story:
  • In 1847, Ignaz Semmelweis drastically cut childbed fever deaths by mandating hand washing with alcohol.
  • His insights were initially rejected due to entrenched medical beliefs and psychological biases (“Semmelweis reflex”).
  • Quote (Michael):

    “For some reason, we have these barriers to accepting new information, even in light of convincing evidence.” [17:12–18:47]

• Modern Analogue:
  • Slow acceptance of airborne COVID-19 transmission.
  • It wasn’t until December 2021 that the WHO officially recognized it.

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4. The Paradox of Hurricanes and Fluid Dynamics

[21:02–25:27]

• Listener Question: Why do large hurricanes form if energy usually flows from large to small eddies?
• Hannah’s Explanation:
  • In 3D fluids (coffee cup), energy cascades to smaller scales.
  • Earth's thin atmosphere behaves almost as a 2D fluid—so energy “cascades” upward, creating larger structures (e.g., hurricanes).
  • “Quasi-geostrophic potential vorticity equation”—her favorite equation name. [23:46]
• Jupiter’s Great Red Spot:
  • A real-world 2D-fluid effect: hundreds of years old, massive storm.

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5. Mathematical Poetry: Limericks with Logic

[27:04–43:22]

• Michael delights in mathematical limericks:
  • Introduces classic and original examples.
  • The art of making equations fit in limerick meter.
• Notable Mathematical Limericks:
  • Lee Mercer’s equation-limerick:

    “A dozen, a gross, and a score,
    Plus three times the square root of four,
    Divided by seven,
    Plus five times eleven,
    Is nine squared and not a bit more.” [29:04]

  • Integration limerick:

    “The integral z squared dz from 1 to the cube root of 3,
    Times the cosine of 3 pi over 9
    Equals log of the cube root of e.”[29:32]

  • Mobius strip limerick:

    “A mathematician confided
    A Mobius strip is one sided.
    You’ll get quite a laugh
    If you cut one in half,
    For it stays in one piece when divided.” [31:56]

  • Hannah, delighted: “That is delightfully nerdy.” [31:56]
• Original Michael Stevens Limericks:
  • On Shapes:

    “The rhombus was keenly aware
    That his side lengths were famously fair,
    But when he brought in his neck,
    All his angles were wrecked,
    And then the poor guy was a square.” [33:00]

  • Zero in Division (three limericks) [36:29–39:01]:
    • On dividing by zero as a non-operation.
    • On zero as dividend (always gives zero).
    • On zero divided by zero as undefined (“any number will do—so we say the whole thing’s undefined”).
  • Hannah appreciates the recurring image of “maths police” policing the zero crimes.

Poems as Memory Tools

• Hannah shares a maths poem by Lewis Fry Richardson on fluid dynamics, tying back to the hurricane discussion:

  “Big whorls have little whorls that feed on their velocity,
  And little whorls have lesser whorls and so on to viscosity.” [35:11]

On Counting, Parental Anecdotes, and Bored Children

• Michael recounts explaining to his daughter why zero is even. [41:01]
• Hannah shares her own children’s exasperation at scientists:

  “Mommy, why are your friends so boring?” [41:46]

Final Personalized Limericks:

• For Hannah:

  “A circle of chips was prepared,
  But filling it, nobody dared
  Till she pointed out with
  No shadow of doubt
  That the area’s just ‘fry R squared.’” [42:37]

• For both hosts:

  “Deep thinking’s a kind of defiance,
  And so was their nerdy alliance.
  Mike was the guy
  And the girl was named Fry,
  And the rest, as they say, is, well, science.” [43:03]

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Notable Quotes & Moments (with Timestamps)

• On the nature of math: “We are in a position where maths is either this, like, massive hallucination... or it really is the language of the universe.” – Hannah Fry [03:25]
• On foundational math proofs: “They wrote a book. And by book, I mean books... These are tomes.” – Michael Stevens [08:38]
• On the uncanny effectiveness: “Equations showing us where to look... That kind of couldn't be the case if math was absolute nonsense.” – Hannah Fry [04:36]
• On acceptance of new scientific ideas: “For some reason, we have these barriers to accepting new information, even in light of convincing evidence.” – Michael Stevens [17:12]
• On two-dimensional atmosphere: “It basically acts like a two-dimensional fluid.” – Hannah Fry [22:40]
• On poetry: “A Mobius strip is one sided. You'll get quite a laugh if you cut one in half, for it stays in one piece when divided.” – Anonymous (read by Michael) [31:56]
• On audience challenge: “If you have any limericks that you'd like to share with us... send them to us.” – Hannah Fry [43:22]
• On children’s reactions to science: “Mommy, why are your friends so boring?” – Hannah Fry [41:46]

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Segment Timestamps

| Time | Segment / Topic | |----------|----------------------------------------| | 02:15 | Introduction to “Fieldnotes” | | 03:02 | Listener Q: Is math correct? | | 04:22 | Effectiveness of math, real-world cases| | 07:26 | Principia Mathematica & math proofs | | 10:54 | Invented vs. discovered mathematics | | 13:56 | Germ theory and Semmelweis reflex | | 19:54 | Modern analogies (COVID transmission) | | 21:02 | Hurricanes, fluid dynamics, 2D flow | | 23:46 | The “quasi-geostrophic...” equation | | 27:04 | Mathematical limericks, poetry | | 33:00 | Michael’s own limericks | | 36:29 | Division by zero limericks | | 41:01 | Anecdotes about kids & zero | | 42:37 | Limericks personalized for the hosts | | 43:22 | Audience invitation, outro |

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Tone & Style

• The conversation is witty, deeply enthusiastic, and occasionally goofy (“maths police,” self-deprecating humor about their own nerdiness).
• Michael and Hannah balance rigorous scientific explanations with playful banter, making highbrow topics approachable.
• Frequent encouragement for audience participation (share your inventions, send in your limericks!).

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For Further Listening

Listeners interested in:

• The philosophy of mathematics
• How scientific ideas take hold (or don’t)
• The hidden dynamics in familiar things (like hurricanes, or numbers)
• Playful intersections between science and the humanities

...will find this episode engaging, mind-bending, and oddly comforting.

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Want More?

• Submit your own mathematical limericks or science questions to the show!
• Watch for future deep-dives as Hannah & Michael threaten (promise?) to do entire series on the philosophy of mathematics and on the number zero.

Transcript

[Hannah Fry]

This episode is brought to you by Cancer Research uk.

[Michael Stevens]

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[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.

[Michael Stevens]

So scientists are studying their biology. Boy, its cancer fighting secrets. It's a reminder that discoveries can sometimes come from places you don't expect.

[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.

[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.

[Hannah Fry]

For more information about Cancer Research uk, their research, their breakthroughs and how you can support them, visit cancerresearchuk.org restiscience.

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[Michael Stevens]

Hello and welcome to the Rest is Science. This is Fieldnotes, a podcast expedition into the minds of Michael Stevens and Hannah Fry. We've brought along some baggage, some luggage, some thoughts, some things. In these episodes we share stuff from the museum of our minds.

[Hannah Fry]

Yeah, then let's, let's delve into that. It's, you know, you sort of think this, I think as like the rest of sciences version of show and Tell. That's, that's, that's the sort of idea that we're going up for here.

[Michael Stevens]

Exactly. But it's like an interactive show and tell because we want to hear and show and tell about you. So send in Your questions, your thoughts, your ideas. And you can be on the show, too, in a way.

[Hannah Fry]

Your crazy inventions, the, the, the darkest depths of your minds. Any of that stuff we would like. And you've got something for us this week, haven't you, Michael?

[Michael Stevens]

Yeah. Later on, I'm going to be sharing something that represents the fusion or it doesn't represent. It is the fusion of math and poetry. Oh, it's poems about math. Okay, but we'll get to that later. First, going to start with you guys. We've got some questions that have come in. I want to start with this one from Noor. This may sound ridiculous, but how do we know math is correct?

[Hannah Fry]

Okay, first of all, I see Noor that you've. You've gone for math rather than maths, which is only adding to the conclusion that we drew a couple of weeks ago. All right. Also second thing to say, not a ridiculous question at all, nor actually quite a deep and insightful question, and one that there unfortunately isn't, isn't really the sort of satisfactory answer that you or any of the rest of the world might be hoping for, because the real answer is that we don't. We don't know that it's correct. And people have tried to. To prove that it's correct. And I mean, basically failed. Failed to do so. One thing I will say is that we are in a position where maths is either this, like, massive hallucination that all of us have come up with that that just so happens to work perfectly, or it really is the language of the universe. That's, that's the sort of the. It's only one of those two things that can possibly be the case.

[Michael Stevens]

It's one of those two things. Yes. What's that famous paper? The Unreasonable Effectiveness of Mathematics.

[Hannah Fry]

Exactly.

[Michael Stevens]

It's like, look, we, we came up with all these rules, and then when you practice them in the real world, it always works.

[Hannah Fry]

I mean, what are the chances? What are the chances that it always works, but not just always works on the stuff you already know about? Always works about the stuff that you don't know about either. So there's loads of examples in science of where there's been an equation, everybody's liked the equation, but there's been something weird that the equation has predicted. So, for example, Dirac was messing around with an equation, and there was one point where it showed that there could be sort of a negative sign where you wouldn't expect one. And that was really the birth of the idea of antimatter, which then was went on to be demonstrated to be absolutely true. There was a group of astronomers who were looking at the path of Uranus in the sky and it was moving weirdly. And they were like, well, we like Newton's equations of gravity, we sort of feel like they do a good job. And so without looking at a single telescope, they sort of worked out what could possibly be going on and predicted the existence of Neptune, figured there must be another planet there that's sort of mucking up this path of Uranus and then indeed managed to find that planet as a result of it. And there are, I mean, there are countless examples of these. Right. Over and over and over again. Equations showing us where to look or showing us something we didn't know about. That kind of couldn't be the case if math was absolute nonsense.

[Michael Stevens]

That's right. And so I think what we're doing here, though, is we are defining correct to mean effective works corresponding to reality. If that's what we mean by correct, then we do it through observation and experimentation. And yeah, I mean, look, we landed people on the moon, we got it right. You know, those equations, those ballistic trajectories, they all worked out. But yeah, math can also explain things that we could never test. We can use math and logic to figure out that we'll never know the answer to something. Yeah, and that's a weird thing when you prove that, like, oh, yeah, it's been proven that this cannot be known under the current framework.

[Hannah Fry]

And that's really, like, what you're hinting at. There is the sort of deep, dark secret lying in the very foundations of mathematics that everyone, I mean, basically tries to not look at too closely, which is that we have tried to prove that maths is correct. There's this. I mean, we should definitely do at least one episode on this.

[Michael Stevens]

Yeah, we will.

[Hannah Fry]

Like, but in the 1900s, people tried very, very, very hard to prove that maths is correct by saying, right, what most. The smallest kind of what are the atoms of maths effectively? What are the axioms? The smallest nuggets of truth that we can, we can take as fact and then build up from there. And, and the only thing that they managed to prove, as you hinted at, is that you can't prove that maths is correct.

[Michael Stevens]

Yeah, and they tried. I mean, we don't. Yeah, we're going to spend a bunch of time on your question or we're going to do a whole episode on it. But I just wanted to show now that I've got my full bookcases here, who Was it was Bertrand Russell worked with someone else, or was it Vonazo?

[Hannah Fry]

Whitehead.

[Michael Stevens]

Yeah, Whitehead.

[Hannah Fry]

Have you got the book? Have you got their book?

[Michael Stevens]

I've got the books.

[Hannah Fry]

Have you?

[Michael Stevens]

So Bertrand Russell and Alfred Whitehead decided we're gonna just finish this once and for all and we're going to prove that one plus one equals two.

[Hannah Fry]

Yeah, okay.

[Michael Stevens]

Without, like, having to go, well, look, if I have one thing and then I have a second thing, one, two, it's two things. They were like, let's do it purely with the mind. And here's how they did it.

[Hannah Fry]

Now, while Michael is getting that book, I'm going to tell you some of the problems that they ran into. Because for starters, to be able to prove that one plus one equals two, you sort of need to know what two is. And it's not enough to just say, oh, well, two is the number that follows one, because that requires, you know what one is. So what they wanted to do was come up with a way to like, define two ness, as it were.

[Michael Stevens]

Yes, you need to know what one is, and you also need to know what follows or comes after means. And so they wrote a book. And by book, I mean books.

[Hannah Fry]

Oh, my God.

[Michael Stevens]

This is the Principia Mathematica by Alfred North Whitehead and Bertrand Russell. And these represent all the characters and words and the new language they had to invent to prove that one plus one equals two. So they did all of this work, and then someone else came along, Godel, and said, ah, but yet there's a little bit of a problem with all of this. And they just, they said, screw it. And so now you can only get this in paperback for people who are.

[Hannah Fry]

Listening rather than watching. What Michael just picked up is, I mean, frankly enough that you could skip an arm day at the gym, right, Just by picking that up. These are tomes. There's three volumes of it. They are thousands and thousands of pages in total. There were supposed to be six volumes in the end, but even look at this, it's impenetrable. I know actual professors of logic who have never read these books because they are so unbelievably dense. You know, I strongly suspect that only Russell and Whitehead are the people who have ever existed, who have ever worked their entire way through those books.

[Michael Stevens]

Yeah, I tried to read it and I said, man, I have to learn a whole new language first. And sometimes you just have to embrace the religious aspect of math, which is that through faith alone, I accept that one plus one equals two. Now let's move on.

[Hannah Fry]

And it sounds like you're being almost flippant or silly by saying that. But really, when it comes down to it, I mean, we're not lying. Honestly, there comes to a point where it really is just a matter of faith.

[Michael Stevens]

Yeah. And so I think we should definitely do a full episode on this because I'm sure a lot of listeners are going, this sounds like the biggest waste of time in human history. Why would you need all of that work, all of these new symbols, all this new way of thinking to show, to prove that one plus one equals two, but it's, it's actually extremely real.

[Hannah Fry]

Yeah, I see. See, I think the other half of listeners is sort of saying, I'm sorry, what, what do you mean you don't know that maths is correct? What, what, what are you, what are you talking about? That once it comes down to it, it's all an act of faith. And, and both of those things are true. It's both. And terrifying.

[Michael Stevens]

Yeah. But it's really effective. Okay. So working and corresponding to reality might be different than correct. Do you. Let me put you on the spot. Do you think that math is discovered and it's been really coincidentally useful, or do you think that it is something very fundamental in the universe's fabric discovered or invented?

[Hannah Fry]

I actually did, a few years ago, I did a three hour documentary series on exactly this question. So you'd better believe I have thought about this extensively. And I think that my final sort of conclusion that I came to is that the tools that we've built are invented. Right. The way that we write numbers, the way that we structure equations, all of that stuff is invented. But what we're doing with those tools, there is no doubt in my mind that it is discovery. And there's this really beautiful description by Andrew Wiles, who was the person who solved Fermat's last theorem. Again, we should definitely do an episode on that.

[Michael Stevens]

Yep.

[Hannah Fry]

He describes doing mathematics that has never been done before. Right. So if you're sort of doing a PhD, if you're doing research mathematics, which I've done, this is really, I think, the best description of what it feels like. He said that it feels like you are, you are clambering through an incredibly thick brush, right through a sort of hedge, and it's incredibly dark. You don't know which way you're going, you're turning around, everything looks exactly the same. And then if you're lucky enough, you will have one single moment where you will turn a corner and instantly before your eyes, you will realize that this entire time you've been navigating this perfectly manicured garden, and you are in absolutely no doubt whatsoever that what you are seeing, all of the places that you visited, how they all fit together, you will be in no doubt whatsoever that it is not of your invention, that you are exploring a space that exists beyond the human mind.

[Michael Stevens]

That's beautiful.

[Hannah Fry]

Yeah. That's why people want to be mathematicians.

[Michael Stevens]

The tools, the machetes you're using to chop through what feels like a dense jungle. We invented those.

[Hannah Fry]

Yeah.

[Michael Stevens]

The symbols, the theorems, the axioms, and. And yet they suddenly just become the frame through which you look and go, oh, shoot, it's wonderfully clear and manicured and was just waiting for these tools to fit into it. Yeah, right.

[Hannah Fry]

We'll do more on that if you want. If you want us to. I mean, look, me and. Me and Michael can basically, we could do an entire podcast series on, like, our love of deep philosophy and the philosophy of mathematics. So, you know, maybe you should tell us whether that's something that you want. But I've got another question in. This one's for you, Michael. This is from Thomas, who asked how difficult was it for the discuss discoverers of germs to convince the world that something they couldn't see was harming us?

[Michael Stevens]

Yeah, it was really difficult. I think a lot about the. And this might be what the. The question asker is getting at, a phenomenon in human psychology known as the Semmelweis reflex. Have you heard about this?

[Hannah Fry]

No.

[Michael Stevens]

So. So, yeah, I mean, germ theory, first of all, germ theory is the idea that illnesses and disease are caused by real things. So not ghosts or spirits or curses, but real mechanical things, biological things that are just too small to see. Okay, so if you can't see them, how do you know they're there? How do you know that an illness is caused by, like, a little organism and not just by bad air or your own sins? Right. Like, it's hard to prove one way or the other. So one of the most famous stories of germ theory slowly being accepted was that 20 years before germ theory became a serious topic of discussion, back in 1847, there was a Hungarian physician named Ignaz Semmelweis, and he worked at this hospital where autopsies were done on every person who died in the hospital. And the doctors did this without, you know, gloves, without proper antiseptic technologies, because they didn't know. But it wasn't great to go to a hospital back then. You often left with brand new infections. You would get better and then you'd get worse. And his theory was that the problems they saw that seemed to only appear at the hospital were truly iatrogenic. That means an ill effect, something bad, a disease caused by medical activity. So caused by the doctors themselves, by the nurses themselves.

[Hannah Fry]

Because wasn't that there was like a maternity ward? There wasn't.

[Michael Stevens]

Yes, there was a maternity ward there. And there was this disease known as childbed fever. And he said, maybe we shouldn't be doing gynecological exams with the same hands we've just performed autopsies with. And he didn't know that there was a virus or a bacteria, any kind of microbe on the hand. He thought maybe it was just the smell, because he said, you know, after you do an autopsy, your hands smell, and if you wash all the debris off with soap and water, they still smell. Right? So it must be this bad smell. And he thought that the smell was made of what he called cadaverous particles. But he found that if he used alcohol, the smell went away. So he instructed everyone at his hospital to wash their hands in really strong, high proof alcohol. And the fatality rate of childbed fever improved by tenfold at only his hospital because of this procedure. So, of course, he wrote about it. He told doctors all over the world, this is back in 1847, that late.

[Hannah Fry]

Oh, my goodness. Because there's the counter to that, is that, you know, in other hospitals. But people were. I mean, it seems wild that you would, like, cut up a dead body and then immediately go and deliver a baby without washing your hands in between. Seems insane.

[Michael Stevens]

Well, the prevailing theory at the time was that childbed fever was caused by miasma, bad air. And so it had nothing to do with the hands of the doctor. And I mean, it was so ingrained as a way of thinking that it couldn't be the doctor themselves. It must be something else. It can't be me. That when Semmelweis spread the results of fatality rates for fever in his hospital and how much of an improvement they'd found, no one accepted it. The experts felt personally insulted, and they just could not change their paradigm. So Semmelweiss's story has been studied profusely when it comes to understanding how people come to rational conclusions, because we don't, Right. We have so many biases, confirmation bias and personal biases and authority bias. All the most famous doctors disagreed with Semmelweis, and they always had. So who's this guy think he is coming in and saying, well, actually, I think that it might be some, like, particles that soap and water aren't getting off our hands. And they said, you're no. Like, why would we believe you? For some reason, we have these barriers to accepting new information, even in light of convincing evidence. And so, again, it took 20 years for people to say, okay, let's start entertaining the idea of these things. We'll call them germs now, and let's do some experiments and take it seriously. So it was a slow process, and we still see that today with accepting new ideas.

[Hannah Fry]

Like what? Like. Like what kind of ideas? I realize I'm putting you on the spot here, but, like, are there some ideas that scientists have been like, guys, seriously, this is a really big problem. And it's just taking people time to accept. The 1850s, I mean, wasn't that long ago, but it sort of feels like this is a lesson that we should have learned by now. Have we or does this still happen?

[Michael Stevens]

Well, yeah. I mean, really recently. How COVID 19 was transmitted, how the virus that caused it was transmitted, took a long time for a consensus to be reached. Despite all the evidence, believe it or not, it wasn't until December of 2021 that the world Health Organization finally recognized airborne transmission of the virus.

[Hannah Fry]

So two years after the first sort of confirmed.

[Michael Stevens]

Yeah, because for so long, the prevailing theory was droplet transmission. That's how they always kind of saw it. They thought, surely it can't waft through the air as well. And it just takes a long time to move something as big as modern science.

[Hannah Fry]

You know, in the center of Mathematical Sciences, where I work at Cambridge. Right. So you've got all of these. These incredible mathematical scientists, people who study how air flows and stuff. They've got, like, this one big lecture theater there. And when the first reports were coming through that it was. It was transmitted by the air, airborne disease. Some of the fluid dynamicists, they took the dimensions of this room, of this lecture room and decided to, like, run this mathematical model of the airflow of, like, what happens when you're standing at the front and basically realized that the exact design of this lecture theater was that anyone who was standing at the front was, like, in direct line of fire. That all of the people's air was, like, perfectly perfect, funneled directly to them. So they. They then redesigned it, and they're these, like, black flags that are up to sort of, like, disrupt the airflow in there still.

[Michael Stevens]

Oh, wow. Yeah. They only want the knowledge to be contagious.

[Hannah Fry]

Exactly, exactly. And also, if there is any contagion, I Think they want it to go in the opposite direction from the professor to the audience, rather than vice versa?

[Michael Stevens]

Ah, yeah, yeah, yeah. Right. Speaking of the dynamics of things moving like liquids, Vin asks, in fluid dynamics, the energy flows from large structures to smaller structures. In that case, why do hurricanes exist? If larger eddies break down into smaller eddies, then no large eddies should ever form. Right.

[Hannah Fry]

What a transition that was, Michael, from germs to floating animals.

[Michael Stevens]

Don't thank me, thank Ben.

[Hannah Fry]

Yes, I mean, that's true. Right. If you think about stirring a coffee, you know, mixing milk into your coffee, you put in your spoon and you're sort of injecting energy at the larger scale. And then the little eddies, the little vortices that come off go smaller, smaller, smaller, smaller, smaller. And that's. It's known as the forward energy cascade. Basically, it's sort of that friction is kind of turning into heat. And in hurricanes, it's the opposite way around that. It's like the rich get richer, the, you know, sort of a winner takes all. The kind of, the little vortices that you get end up cannibalizing each other and growing and growing and growing until you get, get this like giant hurricane. And the reason for that difference, the reason why it's the opposite way around, is it's basically because of depth. So in your cup of tea or your cup of coffee, it's like a three dimensional fluid. But this may come as a bit of a surprise, but in, in the Earth's atmosphere, the Earth's atmosphere is so thin in comparison to the size of the Earth and in particular the spin of the Earth, the Coriolis factory, that it basically acts like a two dimensional fluid. Right. Which is, which sounds like the most crazy idea, but that is basically how we know that it works, is that if you just get rid of that third dimension and you just say, okay, it's a sheet of fluid that is moving around, then suddenly everything works. You can predict the path of hurricanes and so on.

[Michael Stevens]

Oh, wow. I've heard that if the Earth was the size of an apple, the atmosphere would be thinner than the skin of an apple.

[Hannah Fry]

Right.

[Michael Stevens]

It's basically not there.

[Hannah Fry]

It's basically not there. Exactly right. I should tell you the equation that you need when you're trying to work out all of this stuff, this sort of two dimensional flow of fluids on the, on the surface of the Earth, it's got my favorite equation name ever. You know, when you do, you know, when you watch like sitcoms with scientists in it and they Try and make the scientists sound clever by using really complicated words. They. This is my fake sounding, overly complicated favorite equation, which is the quasi geostrophic potential vorticity equation. Ooh, you sound like you're smart when you're saying that. But basically it just means, you know, it's 2D on the earth.

[Michael Stevens]

One more time.

[Hannah Fry]

Quasi geostrophic potential vorticity equation.

[Michael Stevens]

Quasi geostratic geostrophic. Yeah, Geostrophic vorticy.

[Hannah Fry]

Potential vorticity.

[Michael Stevens]

Potential vorticity. Vorticity is a great word, isn't it? It sounds both scientific and literary. Vorticity, the sound and the fury. Vorticity.

[Hannah Fry]

There you go. I should tell you, actually, if you want to see the quasi geostrophic potential vorticity equation, slash two dimensional fluids on the surface of a planet in action, right? And the way that these storms build and build and build and build and build, it's Jupiter that you should look to. There's no solid ground to stop the wind on Jupiter, so it can carry on going, carry on building. Its atmosphere is also very stratified. So it's kind of effectively this 2D wrapping and the great spot on Jupiter. It is this hurricane that has been like, feeding on these smaller storms for, we think at least 300 years. And it's. I mean, it's the ultimate result of what happens in these situations. Thank goodness for mountains, otherwise we'd be in that situation too.

[Michael Stevens]

Yeah, but Jupiter has no mountains, it has no solid ground. But it's. It would seem that its atmosphere would have depth though, right? Like the whole thing is just a big gas giant. Or is it stratified? Meaning there's just thin layers, like an onion that. That can't interact enough.

[Hannah Fry]

Exactly right. They're thin layers that don't interact really enough to make a difference. So it's like exactly as you say. It's like an onion wrapped and wrapped and wrapped. Right. Well, that was quite a massy first half in the end, wasn't it?

[Michael Stevens]

Yeah, it sure was.

[Hannah Fry]

I mean, frankly, I'm happy with it. Let's go into the break and we'll see how matty we get in the second half, shall we?

[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.

[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.

[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.

[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.

[Michael Stevens]

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.

[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.

[Michael Stevens]

All right, welcome back. We had a very mathsy first half, as Hannah said, and we're going to continue to stay mathsy, but we're going to inject a little bit of rhyme, a little bit of art, a little bit of literature. What I've brought today, Hannah, is some mathematical poetry.

[Hannah Fry]

Ooh, delightful.

[Michael Stevens]

And as I was looking through my math poetry books and my own brain, everything I found was a limerick. So, very specifically, these are mathematical limericks. I wanted to share some that you've probably heard before, and then I wanted to show some that I've written just for today's episode.

[Hannah Fry]

What a treat. Okay, go on then. By the way, the chances of me having heard these before is almost zero, because I'm racking my brains and cannot think of a single one that I've ever encountered before. So I think this is gonna be a treat.

[Michael Stevens]

Well, let's see if you've heard this one. This one comes from the most famous palodromist ever, Lee Mercer. All right. You might know Lee Mercer from his most famous work, A man, a plan, a canal Panama.

[Hannah Fry]

No, but the fact that you said that he was a palindrome is making me work out backwards in my head.

[Michael Stevens]

It's a palindrome. A man, a plan, a canal, Panama. So the history of the Panama canal being built can be a palindrome. Same backwards as forwards. But Lee Mercer also wrote this cute little limerick. And a limerick is a kind of poem that has a very specific kind of rhythm. The most famous limerick is, of course, there once was a man from Nantucket, and so on and so on. A lot of them end in a way that is not appropriate for this podcast. But there are clean versions of this Nantucket man.

[Hannah Fry]

I don't know the Nantucket one, but I can imagine what rhymes at the end.

[Michael Stevens]

Yeah. So if you look it up, you'll mainly find, like, clean versions that are pretty clever. But then if you want to find the dirty ones, you'll read them and you'll go, oh, my gosh, that is a lot dirtier than I expected. So here's what I want to share from Lee Mercer. That is a mathematical limerick, not. Not a palindrome.

[Hannah Fry]

It's.

[Michael Stevens]

It begins with this equation. Okay, everyone's looking at this looks like a normal old equation, and yet when we read it, we find the meter of a limerick. A dozen, a gross and a score plus three times the square root of four divided by seven plus five times 11 is nine squared and not a bit more.

[Hannah Fry]

Hang on, let me just work it out. It actually holds. It holds.

[Michael Stevens]

It holds.

[Hannah Fry]

Oh, that's nice.

[Michael Stevens]

It's really nice.

[Hannah Fry]

Gosh, can you imagine how long it took him to come up with that?

[Michael Stevens]

I know, but now let me read you this one, which is from an unknown author. It's an anonymous limerick. I think that in a video, I once credited it to a guy named Matthew on Stack Exchange, but I have since learned that he was just sharing it. He did not write it. So we had Lee Mercer's equation. Now, look at this equation. The integral z squared dz from 1 to the cube root of 3 times the cosine of 3 PI over 9 equals log of the cube root of.

[Hannah Fry]

E. Does it hold? Hang on.

[Michael Stevens]

It holds. It's true.

[Hannah Fry]

It only works in an American accent, though, because if you said DZ then three, you sort of. It falls. It falls apart.

[Michael Stevens]

Okay? But here, let me tell you this. It doesn't have to be Z. It could be T. Let me do a version for the rest of the world. The integral t squared dt from 1 to the cube root of 3 times the cosine of 3 PI over 9 equals log of the cube root of E. That is.

[Hannah Fry]

That is. That is absolutely gorgeous.

[Michael Stevens]

Isn't it gorgeous?

[Hannah Fry]

I'm so genuinely impressed to get it to work so that it actually works as an equation. I cannot even imagine how much time that takes.

[Michael Stevens]

I know, because normally when you write a limerick, you can go, ooh, okay, the meter or the rhyme isn't really working. Let me find a synonym. But in math, you can't always do that. It needs to also work mathematically. Now, it helps that things like DZ or DT3 and E all rhyme. Cosine and 9. That's pretty nice.

[Hannah Fry]

Yeah, but you need the cosine and nine to be in the E bit.

[Michael Stevens]

I know. I know the score.

[Hannah Fry]

And not a bit more. I mean, I'll be honest with you. He might be good at palindromes. That is a tiny bit cheating.

[Michael Stevens]

It's a tiny bit cheating. Yeah, I will admit that too. It's nine squared and not a bit more. It's like, ah, that really. It helped you. It could equal anything. And you could just put on the and not a bit more and finish the rhyme and the meter. Okay, so here's one that's not about an equation. And this one is also from an unknown author. This is an anonymous limerick. A mathematician confided a Mobius strip is one sided. You'll get quite a laugh if you cut one in half, for it stays in one piece when divided.

[Hannah Fry]

That is delightfully nerdy.

[Michael Stevens]

That's really delightfully nerdy. It's very fun.

[Hannah Fry]

Also true if anyone wants to cut a Moby strip in half and have that joy for yourself, then, then, then off you go.

[Michael Stevens]

Yeah, Take a strip of paper, twist one end over, tape them together, cut it in half. It won't be cut into halves. It will just be one bigger loop. Okay, well, here's. Here's one. This is from Dave Morris from an issue of Word Ways. This one is. If you're talking about cheating, this one, it's almost kind of like funny in the way that it works. Here it is. A 1 and a 1 and a 1 and a 1, and a 1 and a 1 and A 1 and a 1 and a one and a one equal 10. That's how adding is done.

[Hannah Fry]

Yeah, that's my kind of guy.

[Michael Stevens]

Still pretty clever.

[Hannah Fry]

It's still pretty good, but it's still pretty good.

[Michael Stevens]

I feel like it's. That's the kind of limerick where once you come up with and a one and a one has the right rhythm, then everything else falls together.

[Hannah Fry]

Wait, did you say that you wrote some yourself?

[Michael Stevens]

Yes, I did. I did. So, okay, here's a geometrical one. Let's do some geometry.

[Hannah Fry]

Wait, are any of them as impressive as that integral one?

[Michael Stevens]

No, none of them.

[Hannah Fry]

They are, though, because you wrote them.

[Michael Stevens]

Thank you, Hannah. Okay, so this one. This one's about shapes. The rhombus was keenly aware that his side lengths were famously fair. But when he brought in his neck, all his angles were wrecked. And then the poor guy was a square. And this plays on the pun that rect R E C T means right. A right angle. A rectangle.

[Hannah Fry]

You nerd.

[Michael Stevens]

Rectangular square.

[Hannah Fry]

That's amazing. Do you know what? I think I actually, this. It's got, you know, there's sort of an anthropomorphization to that. There's like, you know, it's. It's cute. Sort of imagining it in many ways. I prefer that to the other extremely clever ones. It's got.

[Michael Stevens]

Yeah, it's got a character in it. And, you know, I really debated whether I should gender the rhombus are his side lengths or its side lengths. Was the poor guy now a square or was the poor thing now a square? I guess you can make your own decision.

[Hannah Fry]

I like the. I like the guy.

[Michael Stevens]

You like. Yeah, I think it's. I think it's the kind of thing a guy would do. Bring in his neck. And then, oh, my ankles are all wrecked. And now since my side lengths were the same, I'm a square. And it's a great way to kind of teach. I don't know if anyone's going to use it to remember the definition of a rhombus, but, you know, a rhombus is any quadrilateral whose sides are all the same length.

[Hannah Fry]

Yeah.

[Michael Stevens]

Which means a square is a kind of rhombus, but a square is a rhombus with all right angles, rectangles. So that's just a little one for.

[Hannah Fry]

The geometry nerds talking about using poems to remember stuff. And we were talking about Hurricane Zelia. There was a guy called Lewis Fry Richardson, no relation, who was integral in lots of the modeling of hurricanes and weather systems. And he had little rhyme, which was to remember how it all worked, basically. I mean, quite literally talking about hurricanes. He had big whorls have little worlds that feed on their velocity, and little worlds have lesser whorls and so on to viscosity. Oh, isn't that cute?

[Michael Stevens]

That's really cute.

[Hannah Fry]

Yeah. I mean, your rhombus is better, but.

[Michael Stevens]

No, no, there's no such thing as a better or worse poem. You know, maybe there's a more or less successful communication of feeling, but I do feel for this rhombus. It. It should have been happy with what.

[Hannah Fry]

It was, what it was.

[Michael Stevens]

It wanted more respect and so not knowing what to expect. There's different versions of it that I wrote, but I thought that's. That's the one. That's the first version of the rhombus limerick I wrote, simply had his angles become wrecked. And I'm like, ah, but unfortunately, a rhombus with rectangles is Exactly. A square. It needed to be about a parallelogram.

[Hannah Fry]

Yeah.

[Michael Stevens]

It squares up its angles and becomes a rectangle. But parallelogram does not have the right meter to be in a limerick. Limericks have to have dactyls, which means a stressed syllable followed by two unstressed. Oh, yes. For example, there once was a man from Nantucket. Okay. But parallelogram, it doesn't have that little triplet.

[Hannah Fry]

Could you split it, though? Could you go power?

[Michael Stevens]

Yes. You could parallelogram.

[Hannah Fry]

Yeah.

[Michael Stevens]

But then it doesn't scan and people go, oh, you're not very good. So I wanted to share these with you. These are more of like a work in progress. I'm really into division by zero division involving zero. And so I've tried to write some limericks describing the three ways zero can be involved in division. And this first way is when you take some number that's not zero and you divide it by zero. Right. This is like, oh, my gosh, it's gonna, you know, create a black hole and it's gonna end the universe. And this is how I feel about it. Division by zero earns prison. Unless we agree with precision that math doesn't break if there's nothing you take. Because dividing by none ain't division. The idea here is that, look, if division is just. Is repeated subtraction. And I ask, well, if you take away nothing from, say, five, when will I have nothing left? It's like, well, you're not dividing because you're not subtracting. If you're not taking anything away each time, like, it's not a paradox or a weird, you know, singularity inciting event. It's just not division.

[Hannah Fry]

No prison for you. That's essentially where we're at.

[Michael Stevens]

Now, let's talk about when 0 is the dividend. Okay. 0 divided by 5, 0 divided by n. Well, here's the limerick. When 0's the number on top, you don't need a logical cop if you aren't done till the total is none. Just scribble down zero and stop.

[Hannah Fry]

Okay, can I tell you the things I like about this?

[Michael Stevens]

Right.

[Hannah Fry]

One, I like that you are going through the different types of the ways that zero is involved, and you're doing it logically, and it's a progression, and it's great. Two, I like how both of those limericks are tied together by the insistence of there being some sort of maths police. Yes. Who are absolutely eager. Eager to catch people for these zero division crimes. I'm absolutely loving it. Wait, have you got one More.

[Michael Stevens]

There's one more, because there's the special case where 0 is divided by 0, and this is different. So here's that limerick repeated. Subtraction's a grind. But when you see zeros combined, any number will do both, a lot or a few. So we say the whole thing's undefined.

[Hannah Fry]

Oh, that's good. I need a judge in there.

[Michael Stevens]

And for our listeners at home, I think, to appreciate it more, I'm just going to tell you that what's going on there is that we're saying zero divided by zero is asking. Meaning, you know, there's a lot of ways to parse what it means, but one thing it can mean is, how many zeros does it take to have zero? And as it turns out, it could be none or five or seventeen or a billion. That many zeros will always be zero. So it can be any number. And that's why zero divided by zero is undefined. Now, a lot of people say that a number divided by zero maybe is like infinite or something, but even an unending amount of nothing won't ever equal the dividend. So, like, the quotient is just. It's not division. And then finally, when you're. When you're dividing zero by another number, you're asking, like, zero divided by seven, how many sevens will give me zero? It's just none. Easy.

[Hannah Fry]

That whole thing about the number being undefined, zero divided by zero. I mean, I also think we should do a whole episode on zero at this stage. Michael and I really are just doing a whole podcast series on the philosophy of mathematics. But zero divided by zero, sometimes there is actually an answer. Sometimes it's undefined. Sometimes it's infinity, sometimes it's zero. Sometimes it has a finite answer.

[Michael Stevens]

Okay, so, yes, we're going to do an episode on this. You're going to teach me. I'll write some more limericks. And then finally, the division involving 0, Limerick Sonnet, or, you know, a book of poetry, will be complete. Yeah, there's so much to say about zero. For example, my daughter likes me to count by twos when she's going to bed, and I always start at zero, and she's like, is zero even? And I'm like, well, it is for a few reasons. It just helps the pattern work. But also, like, an even number is just two times some integer, and two times zero is zero. So zero is even. And she still doesn't really believe it, so we'll set her right.

[Hannah Fry]

Meanwhile, my two daughters asked their dad the other day, is zero A number. And he gave them an answer. But then when we were all together, he said, oh, you should really ask your mum that question because she'll have something much more interesting to say.

[Michael Stevens]

Yeah.

[Hannah Fry]

And they both declared that they deliberately didn't ask that question in front of me because I would give a boring answer. In fact, because of my job. Right. I know quite a lot of the most amazing science people in the world, right? You, Michael being one of them, Brian Cox being another. I've met David Attenborough, like all of these people, and I've tried over and over again to introduce my daughters to them. And every time I'm like, come on, let's watch one of these programs. It'll be amazing. And every single time they say, mommy, why are your friends so boring?

[Michael Stevens]

Uh huh.

[Hannah Fry]

So, you know, hopefully you dear listeners will find it slightly more interesting than my children.

[Michael Stevens]

I hope so. I mean, my daughter's young enough. She hasn't quite like, become a rebel. So I can still tell her, yeah, look, we're gonna count by twos tonight. And she asks for that. But that's because she doesn't know that there's anything else to talk about. All right, I've got. I've got two more limericks I want to share. And these are about us, okay? So they're not actually mathematical or scientific, really. All right, let's start with this one. I'm not quite happy with this one, but here it is. A circle of chips was prepared, but filling it, nobody dared till she pointed out with no shadow of doubt that the areas just fry R squared.

[Hannah Fry]

I love it. I love it. Yeah, that's great. Also, thank you for using chips as well rather than fries even.

[Michael Stevens]

I know, right? I felt like the kind of like cross Atlantic. The transatlantic combo here deserves fry and chip, so they're both in there. It also meant that I didn't have to repeat the word fry over and over again.

[Hannah Fry]

So that was absolutely brilliant. I'm gonna have that put on my wall. Go on. I want to hear your one, Michael. Go for your one.

[Michael Stevens]

Okay. Well, this was. This is actually about both of us. Deep thinkings, a kind of defiance. And so was their nerdy alliance. Mike was the guy and the girl was named Fry. And the rest, as they say, is, well, science. Yay.

[Hannah Fry]

They are so good. They are so good. We have found a new skill. We have found a new skill from Michael Stevens. If you have any limericks that you'd like to share with us. Any others? I think, Michael, you need your own one. I'm gonna between now and the next episode, I'm gonna, I'm gonna furiously start scribbling. I don't think I've ever written one in my entire life. So that we're gonna really test your theory on whether it's possible for there to be a good or bad poem once. Once I come back to you with that. But I think that concludes our episode for the day. If you have anything you'd like to send us in limericks or otherwise send them to us. Theres scienceoalhanger.com yes, and please join our.

[Michael Stevens]

[e-mail] Science we'll be back next Thursday.

[Hannah Fry]

With another episode of Field Notes and on Tuesday with our normal episode. See you then.

[Michael Stevens]

See ya.

[Hannah Fry]

Foreign.

[Dominic Sambrook]

It's Dominic Sambrook here from the Rest.

[Gordon Carrera]

Is History and Gordon Carrera from the Rest Is Classified.

[Dominic Sambrook]

Now, over the last month or so, the regime in the Islamic Republic of Iran has been pushed to the edge, having seen the largest protest for a generation ripping across the country. Tens of thousands of people have been killed by the Ayatollah's forces since the uprising began, and a lot of people outside Iran are asking, is this the beginning of the next Iranian revolution?

[Gordon Carrera]

And Goal Hanger is covering every element of this. On the Rest Is Classified, David and I have looked at the role of intelligence agencies in this conflict. With the Internet blackouts and so much unknown, we've been looking at whether spies are best placed to judge whether the regime is truly at risk of falling.

[Dominic Sambrook]

Now on the Rest Is History, we have been looking at the origins of of the Iranian regime at the 1979 Iranian Revolution, which saw the fall of the last shah and his replacement by the rule of the ayatollahs. Now, given that the last shah's son is being touted abroad as the man who might, just might, save Iran, you can't understand what is happening now without understanding what happened back then at the end of the 1970s.

[Gordon Carrera]

But it's not just our own two podcasts that are covering Iran. If you want to know whether Donald Trump's military buildup in the region means it's likely he's going to wade in and force regime change. Here Alistair Campbell and Rory Stewart cover the latest developments in the Rest Is Politics.

[Dominic Sambrook]

And our dear friends at the Rest Is Money have been looking at the economic collapse, the corruption and the impact of the sanctions that have been eating away its social cohesion in Iran over recent years and have pushed so many people onto the streets and on Empire.

[Gordon Carrera]

They'Ve been looking at the similarities and differences between 1979 and today. How is it that a country that less than 50 years ago forced the Shah out of power is now seeing crowds chanting Long live the Shah?

[Dominic Sambrook]

So whatever happens next, to the people of Iran and to all those brave souls who've turned it on the streets to protest, stay tuned to Goal Hanger for all the context and the answers and the analysis that you need. Find. The rest is history, the rest is classified empire. The rest is politics and the rest is money. Wherever you get your podcasts.