Summary
In this Field Notes episode, hosts Michael and Hannah explore mathematical and astronomical objects, discussing ellipses, planetary motion, and color theory through hands-on demonstrations. They also answer listener questions about famous scientists they'd invite to dinner and debunk the myth that goldfish have three-second memories.
Insights
- Historical resistance to scientific truth: Kepler's discovery of elliptical orbits faced opposition because Greek philosophy idealized circles as perfect, showing how cultural bias can delay scientific progress
- Physical objects as teaching tools: Tangible demonstrations (ellipsographs, orrery calendars, CMY cubes) make abstract concepts like orbital mechanics and color mixing more intuitive and memorable
- Common misconceptions persist due to convenience: The goldfish memory myth likely persisted because it justified poor pet care practices, suggesting misinformation can be socially reinforced
- Brilliant minds under pressure: Galois's most foundational mathematical work emerged the night before his fatal duel, raising questions about whether mortality focuses genius or if it's coincidental
- Science history is filled with eccentric personalities: From Tycho Brahe's prosthetic noses to Pythagoras's bean phobia, personal quirks and dramatic deaths characterize many historical scientists
Trends
Tactile STEM education gaining traction: Physical, hands-on objects for teaching abstract concepts are becoming more valued in science communicationDebunking persistent scientific myths: Popular misconceptions about animals and science require active correction through media and educationHistorical scientific narratives being reexamined: Stories of famous scientists are being scrutinized for accuracy and contextSustainability in educational products: Eco-conscious manufacturing (compostable paper for calendars) becoming standard in science education toolsInteractive science communication: Podcast format with physical object demonstrations creates multi-sensory learning experiences
Topics
Elliptical orbits and planetary motionHistory of astronomy and Kepler's lawsMathematical history and Galois theoryColor theory and CMY color mixingCentrifugal force and rotational physicsGoldfish cognition and animal memoryHistorical scientists and their deathsScience education tools and demonstrationsRadiotherapy and cancer treatmentBlood testing and proactive health monitoringRoller coaster physicsArchimedes and ancient mathematicsPythagoras and ancient philosophyEinstein's brain and neurosciencePet care and animal welfare
Companies
Makis Cabinet
Created the brass ellipsograph device demonstrated in the episode for drawing ellipses using linear motion
People
Johannes Kepler
Mathematician who discovered elliptical orbits after analyzing Tycho Brahe's data, overcoming cultural bias toward ci...
Tycho Brahe
Astronomer who collected extensive celestial observations in the late 1500s; lost his nose in a duel and wore prosthe...
Évariste Galois
19-year-old French mathematician who developed foundational Galois theory the night before dying in a duel over a lover
Archimedes
Ancient mathematician who prioritized circles over his own safety, killed by a soldier during invasion while refusing...
Pythagoras
Ancient mathematician famous for Pythagorean theorem; allegedly died refusing to run through a bean field while being...
Albert Einstein
Physicist whose last words in German were lost to history; his brain was later forgotten in a medical facility cupboard
Quotes
"Swallowing that heap of dung really moved us forward."
Hannah (discussing Kepler accepting ellipses over circles)•Early episode
"Don't disturb me when I'm with my circles."
Michael (quoting Archimedes' alleged last words)•Mid-episode
"I think that this is a massive misconception. I was wondering if that might be."
Hannah (on goldfish memory myth)•Late episode
"The combined distance from that point to both focus is fixed."
Hannah (explaining ellipse geometry)•Early episode
"You idiot. You idiot."
Michael (on what he'd tell Galois at a dinner party)•Mid-episode
Full Transcript
This episode is brought to you by Cancer Research UK. Dinosaurs walked the earth 180 million years ago. But you know, cancer was part of their story too. Scientists have found tumors in ancient fossils. Well that is part of the reason why cancer is a big part of our story, right? It's the other side of evolution. It's the most complex disease that we face. There are more than 200 types of cancer in total, each with distinct characteristics, challenges and mysteries. And that complexity demands scale. Cancer Research UK is the world's largest charitable funder of cancer research, with more than 4,000 scientists, doctors and nurses working across more than 20 countries in the search for answers. And then sharing their discoveries beyond borders. And the impact of this collaboration is clear, because over the last 50 years, the charity's pioneering work has helped to double cancer survival in the UK. That is more people who are living longer, better lives. Bossels can show us the past, but research is shaping the future. And for more information about Cancer Research UK, their research, breakthroughs and how you can support them, visit cancerresearchuk.org forward slash rest is science. This episode is brought to you by Project Hail Mary, the new spectacular space adventure coming to cinemas. Okay, hypothetically, imagine that there's this mission to save our world. Only you can do the job. As this expert in mathematics and science, how do you think you would do? Terribly, but not because I love teaching and learning, because I'm a scaredy cat. But what about yourself, Hannah? I'd back myself, Michael. I think I'd be good. I just, I'd just be very slow. I think the point is that no one should rely on Hannah or I to save the world. But in Project Hail Mary, Ryan Gosling stars as science teacher Rylan Grace, who is sent unexpectedly on an impossible mission to space to discover why the sun and stars are dying. He teams up with an unimaginable ally to defy all odds and save the universe from extinction. See Project Hail Mary in cinemas and IMAX from Thursday the 19th of March. You can also catch it early on Saturday, the 14th of March, Pi Day, and Sunday, the 15th of March. Hello and welcome to The Rest is Science. Today is an episode of Field Notes, where Hannah and I share amazing stories, objects, our deepest fears. Oh, we're going there today. We might be or we might not. If you have questions or things you want to share with us, you can always reach out. We would love to take on those. But today, Hannah told me that she brought something related to ellipses. I did. Okay. If you want to draw a circle, easy peasy, get a compass. Hold on. I want to guess what you brought. You've already given me a piece of information that's almost confirming what I was going to guess. Oh really? Okay, let's imagine I didn't go. Okay. Is it an ellipsograph? It might be. Is it just an ellipsograph? Is it allow me to draw an ellipse or does it simply trace an ellipse in a surprising way? It allows you to draw one. But I think in a surprising way, I think in a very beautiful way. Is it a circle that rolls on the inside of another circle? No. Okay. Let's see it. Okay. You want to draw a circle, you get the compass from your primary school pencil case that you have not opened since and never needed to use in actual real life. And that's fine because you just, a circle is a fixed distance from a single point and trace out the arc, right? Yeah. Easy peasy. Ellipses way harder, way harder because instead of having one focus, you have two and you can do it by putting two pins into a piece of paper and like tying a single piece of string between the two and then using a pencil to kind of trace out that arc. That is one way of doing it. So some friends of mine at Makis Cabinet have over engineered a way to draw ellipses and I thought you might enjoy it. Yeah. You know, you sort of, this is sort of like a draftsman in you somewhere. Yeah, there is. The key point here is that an ellipse is a fixed distance between two focus, okay? Between two points. So what does that mean? That means that no matter where you are on the ellipse, the combined distance from that point to both focus is fixed. Is the same. Exactly right. Got it. Okay, so do you want to have a little play with this? Yeah, I can get it. It's work. Okay, okay. So, so there's a magnet. Oh, that's a nice strong magnet. There's a magnet underneath this page. This sits on it. Ah, yeah. I wanted people to appreciate this ellipsic graph. Look at this. Those shuttles are following straight line tracks and yet we trace out an ellipse from circular motion. Well, from linear motion, we get circular motion. I love that. It's so well made. It's beautiful, isn't it? I've seen them made of wood and plastic, but this is like brass. Look at that. Isn't that beautiful? Come on. What a treat. I mean, isn't that a treat? Yeah. They're the coolest objects. They're how the planets move. They are how the planets move, but the thing is that there was such big arguments about the idea that that is how the planets move because the Greeks in particular were obsessed with circles. They thought there was like the platonic ideal, the symmetry of it, the beauty of it. It's just absolute perfection. This stood for a really long time, this idea of circles. I mean, like thousands and thousands of years, people thought it's circles that's going on in the sky. And then Tico Bra or sometimes people say Tyco don't know. I say Tyco. I say Tyco, bra. From now on, that is how we're all we know. And he was a bit of a bra actually, because he got into an argument with someone about a formula. He had a jewel, ended up losing his nose. No kidding. You know this, right? I didn't know this. So he lost his nose, so he had a prosthetic nose. He had different ones. He had a bronze one. He had a silver one for special occasions. And then a gold one that flickered in the candlelight to look realistic. He collected all of these observations of celestial objects in the sky. He also had a pet elk that he used to bring around to places. In the end, the elk passed away because it got drunk. Oh no. Got the elk drunk and tried to take it downstairs. Anyway, whatever. He was a bit of a dude. Yeah. This was in the late 1500s. Exactly. Exactly. At least 1600s, exactly. And he collected all of these observations. And he handed off all of that data to his assistant, Kepler. And Kepler was like looking for the circles, looking for the circles, trying this circle, that circle. And then eventually came to the conclusion that no, it's not circles, it's ellipses. And he said that it was like a cartload of dung that you had to swallow because he just hated, hated the idea that there might be anything other than circles in the sky. But it was. But it was. Swallowing that heap of dung really moved us forward. It really did. Imagine that being like, oh, here's my assistant Kepler. Like, can you imagine better help? Speaking of the motion of planets as perfect because I actually brought something related to them. Now, this shows them in circular orbits. Sorry, Kepler, but it's a simplified thing for a reason. Watch. This is an orary calendar. It's a page a day calendar. It doesn't tell you an inspirational quote for each day or give you a Sudoku for each day. It shows you the relative positions of the planets each day. This is January 1st of 2026. It's a 2026 calendar. And then the next one is we actually got two of January 1st. And then the next one is Friday, January 2nd. And as you can see, almost imperceptible, almost don't change. However, you use it like a flip book and you can see just how quickly the planets are moving in their orbits. Okay, show, show, show, show. So Neptune basically doesn't move at all in a year, but Earth goes all the way around once. Okay. Now, full disclosure, you can only flip it backwards easily. You kind of have to like break the back. Oh, that is amazing. But isn't that cool? So you can plan ahead and be like, oh, I want to do that thing, but only when Uranus is as far away from Earth as it's going to be all year. And then they've got the moon phases on them. It sort of feels like more than 360 pages, but it isn't. Well, we made it out of a special recyclable paper, like a compostable paper, because I was like, if we're going to print this many sheets, I want to keep Earth happy. That is absolutely delightful. Mercury whizzing around there. I know, isn't it nuts? And Jupiter just barely, I mean, it's taking its time. Jupiter takes its time to go around the sun, but around its own axis, Jupiter is like really fast. It takes the Earth 24 hours to go once around its axis, but it takes Jupiter just 10 hours. So it's two and a bit days for every day. That's wild, because Jupiter is huge. So if you are some gas out on the edge of Jupiter around the equator, you are booking it. Like no wonder that Great Red Spot won't go away. The storms on Jupiter have an enormous amount of energy just from that planet whipping it around. It's just making the idea of being on a spaceship and just your face being pulled back with the speed of it. Well, I mean, it's not quite that fast. I mean, none of us are on Earth being like, whoa, even though we are rotating at, you know, hundreds of miles per hour around its axis, Earth is just too big even for us to appreciate that. Don't ruin my memory. It does make us a little bit lighter in the same way that when you're on a spinning carnival ride, you feel like you're being pulled away. Really you're being pulled tangential to the circle. But on Earth, we are feeling that motion too. And so we weigh a few fractions of a gram less because of its rotation. And if it stopped moving, we'd be like, oh, all of the gravity. I'm feeling all of it. So wait, what's that on Jupiter then? So you're spinning faster, but it is heavier. You're spinning faster. So you've got an even greater like uplift. We often call it a centrifugal force when it's not really a force, but it's that like, oh, I'm moving away from the center of rotation of my curve. When in reality, you're leaving tangential to the path. But on a big circle, that feels like going straight up. There's a ride at Thought Park. And what's interesting about it is that it has the longest negative G, basically. So you are effectively airborne, if you like, in your seat. But the way that they have to do it, you know, normally you are, as you go on a roller coaster, you are forced into your seat. So you want to go down. It's like, you know, like really feel the weight of it. In this one, it's the opposite. And the way that they do it is they have to slow down the carriage as it goes on the outside of a turn in order for you to really have that feeling of being flung out into the air. Whoa. I won't be riding on that anytime soon. I don't know. I just I never had as a kid, I actually collected newspaper clippings of deaths on roller coasters. Because it made me feel like my fear was justified. I still have the box. It's actually the box that my Bill and I fan club subscription goodies came in. And then I just put little comics and recipes and deaths at the Worlds of Fun Theme Park in Kansas City all in there. Please one day, can we do a field notes when you go through that box? Yeah, we sure can. It's going to be a lot of like corny family circus cartoons that I thought were quite clever when I was eight. But I brought I brought one more thing. This is actually for your two daughters. OK, amazing. You you better believe I'm stealing this, by the way, just to be absolutely clear. You cannot steal that because I have to make a video about it. And it's the only one I have. Fine. I will get you one that can be just yours. Here's two C.M.Y. cubes. These are the additions that we put in a curiosity box as if I'm going to buy anything for you. But route. The couple who invented those are fantastic people. And we partnered with them to make this addition of their C.M.Y. cube. It is a translucent cube about two inches on each edge. And opposite faces of the cube have the same color, the same translucent color. And the colors that you'll find are there's three of them, cyan, magenta and yellow C.M.Y. Those are primary colors in the C.M.Y. system. And you can combine them to make all kinds of other colors. You've got magenta, then twist it. You've got yellow and then twist it again. And you have got cyan. Cyan. I mean, is it the colors you get in your printer? That's right. But if you combine them together. Hang on. Does it work? Does it work? It does work. Yeah. I'm just trying to work out what the colors. It can be very confusing because there's not just the subtractive color mixing that's happening. There's also reflection, but greens and purples and oranges are produced as the light is subtractively changed. Passing through the cyan filter, only cyan comes through. Hey, do you know where you send naughty rainbows? Where? To prison. I do. I do like that prisms can create rainbows, but they can also destroy them. If you send a prism through a rainbow, it comes out as white light. Does it? Yeah. And if you look at a rainbow, like a rainbow in a children's book through a prism at the right distance, it'll get smashed into just a white line. Yeah. These are absolutely amazing. They're really beautiful and they're really well made. Also, what I notice is like the sorts of truth. This is the second object that you've given me for my children with extremely sharp edges. Oh, that's right. Yeah. You're welcome. Amazing. Should I get a break? Let's take a break. This episode is brought to you by Cancer Research UK. Radiotherapy is over a century old, but it is still changing. Cancer Research UK helped lay the foundations of radiotherapy in the early 20th century and has driven progress ever since. Radiotherapy remains one of the cornerstones of cancer treatment today. Every year, millions of people worldwide benefit from Cancer Research UK's work to make it more precise. Scientists are still refining how radiotherapy is delivered. And one example is an experimental treatment called flash radiotherapy, which delivers radiation in fractions of a second up to a thousand times faster than standard radiotherapy. And early studies suggest that speed could make a real difference. Flash radiotherapy may cause up to 50 percent less damage to healthy cells. But scientists don't yet know why healthy cells seem to be spared. So Cancer Research UK are working to answer that. Understanding it could be key to reducing side effects in the future. For more information about Cancer Research UK, their research and breakthroughs and how you can support them, visit cancerresearchuk.org forward slash the rest is science. This episode is brought to you by Thrive. Most of us tend to think of blood as something slightly clinical, linked to illness or bad news. But in reality, it has been quietly keeping a record of what's going on inside our bodies, almost like a biological diary. It holds clues about how everyday choices shape our health. Sleep, stress, food, movement. And without access to that information, staying healthy can feel more complicated than it needs to be. Thrive is a proactive health platform that lets you check in from home using regular at home blood testing with clear guidance to help you understand what your body is telling you. That sense of clarity changes how health feels. Instead of juggling advice, rules and trends, you get a simpler sense of direction. What looks consistent, what's shifted a little and what's actually worth paying attention to. It just makes health feel calmer and simpler to think about day to day. Head to Thrive.co to get started. That's T-H-R-I-V-A-dot-C-O. And use code TRIS for 20% off your first test. Welcome back. This is Field Notes, an extra half an hour that you get to spend in the company of me and Michael every single week, where we try and impress each other with things that we know, things that we found. I'm not trying to impress you with any of this. Oh, I'm absolutely trying to impress you. I'm trying to impress my mom. Yeah. Aren't we all? Aren't we all? Anyway, sorry, this got really... Deep. Deep very quickly. Let's lighten it up. Who's got a question? Should we go to the mailbag? Yeah. OK. All right, we've got some interesting questions this week. By the way, please do feel free to send in your questions to the rest of science at goalhanger.com. All right, Alana asks, You can invite three other people from the world of science who are dead or alive to a dinner party. Who you choose in? Oh, my gosh. Do you have an answer? I mean, I've definitely got some favorites. Yeah, sure, sure, sure. I feel like, you know, Albert Einstein is one of the more obvious cliche types of answers, but I want to know what his last words were. You know, he spoke them in German to a nurse who did not know German. And so they've been lost. No. I want to know if it was like, oh, crap. Or if it was like, oh, it's actually MCCube, you know, or something. I don't know. But I would love to find out. I'd also like to know how he feels about, you know, the story about Einstein's brain. Oh, his brain. Yes. And then it was sort of extracted, put in a jar and then just forgotten about. That's right. It was in the back of a cupboard and someone found it years later and we're like, what is this? And it turned out to be Einstein's brain. And this was at like a medical facility, by the way. It wasn't just like, oh, his neighbors came over and put it out. It was like donated to be studied and then just forgotten about forgotten about. Yeah. In a little medical closet. But when they did study it, they basically found there was nothing remarkable about it, right? So maybe slightly more white matter than the rest of us. I'd like to ask about that. I would like to ask about that. How do you feel about your brain being forgotten about in a cupboard for a very long time? OK, so besides Einstein, who's on your list? OK, I would quite like to meet Galois. Who is that? OK, so Galois is like, he's such a dude. He's this French mathematician. He's like 19, 20 years old and he is super, super, super bright. But he's also very French and loves to have affairs with beautiful women. One of the people he has an affair with turns out to be engaged to some very important soldier in the town. Who challenges him to a duel. And of course, because he is very French and this is, you know, around 1700s, you can't turn down a duel. So he agrees to go off and have the duel, have the fight with this, you know, with his lover's partner before he does that. He decides he needs to finish his maths theory. OK. So he stays up all night and he scribbles this stuff down. And it's all about, you know, you have quadratics, which is where you have where you have something squared. You have you have cubics, which is which is cubed to the power of three. But he was looking at quartics and quintics. So equations to the power of five, right? I'll be honest with you, it gets very hard very quickly. But so he's he's there. He's like, I've got to I've got to work out these equations. I've got to work out these equations. And we still have the kind of ink splattered pages that he wrote on that night every now and then he's like, he's scribbling down the theory, he's crossing stuff out. And he's right. And then he writes like La Femme, La Femme. And then he's like, oh, I'm going to die in the morning. So I've got to go back to these equations. Anyway, he goes off, jails the jewel. He loses in the jewel, loses his life. But those pages and the work that he did in advance of that then goes on to be absolutely foundational. And now every person who goes to study mathematics as a degree level will learn Galois theory. This 20 year old kid. What a romantic story that is. Wow. It's like if he'd been given just a couple more days, what else could he have discovered? Or was it the impending possibility of death that made him work so well? It just spilled off all that brilliance at once. I just like to meet him at dinner and be like, you idiot. You idiot. That would be very cool. Can we go to the same dinner party together? OK, so we've got Einstein and Galois. We could go we could go way back in time. Like I'm thinking about a Pythagoras would be neat. This is sort of the world of math at this point. But like I want to hear about the the meaning of numbers to him. What do they mean to you? It was much more religious. He didn't really like numbers. I mean, they didn't really like numbers at all, the Greeks. Not all of them. Sure. Those irrational ones. Those irrational ones, they weren't so happy with. They were like the demons. Obviously, Archimedes, I think it'd be cool just to say that I met him. I love that of all the things Archimedes did, the inventions, the Eureka. I'm in a bathtub and I've learned about volume and how to measure it. The story goes that on his gravestone, do you know what he had them put there? Go on. A sphere, a cylinder and a cone of equal heights. Because he showed the relationships between their volumes. And he was so proud of that, that he was like of everything I did. I want that to be what's on my grave. He's Archimedes, the one who died at the hand of a soldier who was trying to capture him. I think there was some sort of invasion of his island. And then he was told to, because he was such a genius, they were going to capture him and bring him back to the whatever, king, something. The soldier went in and was like, you need to come with me. And he was like, don't disturb me when I'm with my circles. And so the soldier killed him. Wow. Yeah. For the circles. For the circles. He just couldn't give them up. Yeah. Maybe instead of doing like, maybe instead of picking people based on the interesting things they have to offer, maybe we should just get the people who've got the most stupid deaths in science. Yeah, right. And we can just make fun of them. Just make fun of them. You could bring Archimedes and then have a bunch of circle foods, OK? Slices of bologna, pie pizzas and be like, hey, let's cut them up. Let's make some cords, some diameters. In your honor. In your honor. Here is this, here's a cone shaped cake. So yeah, it's not so much to learn from them, but it's to honor them and kind of razz them a bit. Yeah, I'd be up for that. That sounds like a good dinner party. Actually Pythagoras himself, he's got an amazing death. Do you know about Pythagoras' death? No. OK, so I mean, this is possibly apocryphal, but I'll be honest with you. A lot of stories that old are. Sure. Yeah. Right. Pythagoras of triangle fame, absolutely amazing. Had a school basically like had loads of, you know, disciples. Terrified of beans, really, really hated them. Thought that they looked like sort of miniature humans. Just really, he absolutely abhorred them. Yeah, who hasn't thought that? He hasn't thought that. Beans were banned in his school. Got it. And the rumor goes that he had sort of a fight with some other people. They wanted to join your school, you didn't let them. They barricaded his house, set it on fire and he ran away, managed to get free, ran away and they were chasing him and then he carried on running. And it was all fine until he came up to a field of beans and he refused to run through the field of beans as they caught up with him and killed him. Wow. This sounds like a great dinner party. Beans and pizza for dinner. Would you bring beans? Yeah. Would you not bring beans? Bean pizza, bean cookies, like a can of refried beans as a cylinder. Archimedes would love that Pythagoras wouldn't. But you know, he's got a he's got a lot of credit. It's time for him to get a little. Roasting. Roasting. That's right. That's right. Well, we've got one more question. This one is from Fred. Fred asks, why do goldfish have such short memories? OK, I think that this is a massive misconception. I was wondering if that might be. Yeah, I think that actually there have been experiments with goldfish where they can sort of, you know, be shown to navigate a maze to get food and then can remember the route that they've learned months afterwards. So where did this misconception start? I think it's just snobbery. Right. It's just straight up snobbery. But also it really does, I think, underline the cruelty of putting a goldfish in a bowl where it's got nothing to do. Because, of course, if it's only got a three second memory, who cares that it doesn't have anything to interact with? But I mean, we did an episode about boredom. All this time, there's pretty little goldfish that we've been having to effectively decorate our homes. We've been essentially torturing them. Yeah, I don't know what kind of space they need. But yeah, a three second memory seems pretty made up. Maybe to make us feel better about like, oh, yeah, there's not much to do there. But yeah, I don't know how much room they need. They might even need like a place where they feel like they can go to be safe and hidden like a little, you know, rock cave feature. Maybe a goldfish friend. A goldfish friend. Yeah. Do they like having friends? I think they do. I think they are quite sociable. Yeah. Yeah. I've never owned one of you. I might have had one when I was like four. Because I kind of remember fish, but not since then. My daughter really wants a bird. Oh, yeah. And I'm like, birds deserve to be free. Not going to happen. So I had a cockatiel when I was younger. What was interesting about him is he would sit on your shoulder in the garden. Oh, outdoors and not leave and not leave. I think you can bond with the bird. I think that's my point. I think you can bond with the bird. I believe that for sure, for sure. And you guys can bond with us by joining our newsletter at the rest is science at goalhanger.com.