Something You Should Know - What Makes a Hit Song & Why You Never See the Same Rainbow Twice

Episode Date: December 22, 2025

If you fall short on sleep, can you really “catch up” the next night? Many people think so — but our bodies don’t quite work that way. This episode begins with what science says about recovering from poor sleep and how to optimize deep sleep when your schedule gets disrupted. https://www.womenshealthmag.com/health/a40511210/deep-sleep/ What makes a song a hit? Trends, personal taste, timing, and luck all play a role — but today, technology shapes popular music more than ever. From how songs are created to how they spread, the path to a hit is constantly evolving. Chris Dalls Riva joins me to unpack it all. He’s Senior Product Manager at Audiomack, a musician and writer, creator of the newsletter Can’t Get Much Higher, and author of Uncharted Territory: What Numbers Tell Us About the Biggest Hit Songs and Ourselves. (https://amzn.to/4pODklu). All kinds of things can be explained by math – from the beauty of a rainbow to the incredible pattern of sunflower seeds to why we have some left-handed people but not too many. Joining me to drill into the numbers on all this is Eddie Woo. He is the head mathematics teacher at Cherrybrook Technology High School in Sydney, Australia. In 2012, he began recording his lessons and posting them on YouTube and created Wootube https://misterwootube.com/ which has more than 600,000 subscribers and over 33 million views. He’s also author of It’s a Numberful World: How Math Is Hiding Everywhere (https://amzn.to/3KOHPOb). There are 12 core workplace skills that shape how well we perform — and everyone has strengths and weaknesses across them. Understanding yours can make a big difference in how you work and how others work with you. Insights come from Chuck Martin, author of Smarts.(https://amzn.to/3KzlaWc) PLEASE SUPPORT OUR SPONSORS! INDEED: Get a $75 sponsored job credit to get your jobs more visibility at ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠https://Indeed.com/SOMETHING⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ right now! QUINCE: Give and get timeless holiday staples that last this season with Quince.  Go to ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠https://Quince.com/sysk⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠ for free shipping on your order and 365 day returns! AG1: Head to ⁠⁠⁠⁠⁠⁠⁠⁠https://DrinkAG1.com/SYSK ⁠⁠⁠⁠⁠⁠⁠⁠ to get a FREE Welcome Kit with an AG1 Flavor Sampler and a bottle of Vitamin D3 plus K2, when you first subscribe!  NOTION: ⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠⁠Notion brings all your notes, docs, and projects into one connected space that just works . It's seamless, flexible, powerful, and actually fun to use! Try Notion, now with Notion Agent, at: ⁠⁠⁠⁠⁠⁠⁠⁠https://notion.com/something⁠⁠⁠⁠⁠⁠⁠⁠ PLANET VISIONARIES: In partnership with Rolex’s Perpetual Planet Initiative, this… is Planet Visionaries. Listen or watch on Apple, Spotify, YouTube, or wherever you get your podcasts. SHOPIFY:  Sign up for your one-dollar-per-month trial and start selling today at⁠ https://Shopify.com/sysk Learn more about your ad choices. Visit megaphone.fm/adchoices

Today on Something You Should Know, can you really catch up on the sleep you've missed? Then how a song becomes a hit and how technology is changing the music business. Actually, song titles have gotten shorter. If your song title is too long, it's going to get cut off on the phone display. It seems artists want people to be able to see the entire title, and because of that, they've shortened them. Also, the skills you need at work that, predict your likely success and fascinating explanations that reveal how the world works. From left-handed people to sunflower seeds to the shape of a rainbow.

The shape of a rainbow is not just half of a circle. It is actually a full circle and that circle is the shape of the rainbow that you and I see. It's just that we usually only see half of it because the horizon is blocking its path. All this today on Something You Should Know. of the regency era you might know it as the time when bridgeton takes place or it's the time when jane austin wrote her books the regency era was also an explosive time of social change sex scandals and maybe the worst king in british history vulgar history new season is all about the regency era the balls the gowns and all the scandal listen to vulgar history regency era wherever you get podcasts Something You Should Know, fascinating intel, the world's top experts, and practical advice you can use in your life. Today, Something You Should Know, with Mike Carruthers. Have you ever not gotten enough sleep one night and figure, well, you know, I'll make it up on the weekend?

Is that a real thing? Does that really work? Well, that's what we're going to start with today on this episode of Something You Should Know. According to Dr. Janet Kennedy, she's a psychologist who treats people with sleep disorders, the idea of catching up on your sleep doesn't work. Sure, if you only got, say, two hours of sleep one night, you may want to sleep in a bit the next day, but in the long term, it's really not about the math. If you are chronically sleep deprived, you will never make up all the hours of sleep you've missed, and you really shouldn't try.

It's about your routine. When you disrupt a regular sleep routine by staying up late, you confuse your body. You may have to take a nap or drink caffeine to stay alert, which causes more confusion to your body. In fact, it turns out you cannot catch up on sleep, but you can even it out. And you do that by sticking to a regular sleep schedule as best you can, weekends included. And that is something you should know. Popular music is often called the soundtrack of our lives. And it sounds a little cliche, but cliche or not, it's true.

Music shapes our memories, our moods, and our culture. And what's so fascinating is how popular music has evolved over the last several decades. Not just the sound of the songs, but the entire way music is created, distributed, and consumed. A lot of us remember having shelves full of records and CDs, but today most music lives on a phone and it's delivered instantly through a streaming service. That shift in technology hasn't just changed how we listen. It's changed the music itself in surprising and profound ways.

Chris Dalariva is here to explain how it all happened. He's senior product manager at the music streaming platform Audio Mac. He's also a musician and a writer who's been featured in the Economist, Business Insider, and the Wall Street Journal. He writes the acclaimed newsletter Can't Get Much Higher, and he is author of a book called Uncharted Territory, what numbers tell us about the biggest hit songs and ourselves. Hey, Chris, welcome to something you should know. Thanks for having me. I'm really happy to be here. So when I think about popular music, popular songs, it seems that a significant number of those songs,

are about love and heartbreak and romance and people falling in love. And is that my perception, or is that really true? I think in broad strokes, that's true. I mean, if you were to turn on the radio today or turn on some oldie station, you're certainly going to hear tons and tons of songs about love and heartbreak and all those related topics, because people seemingly for thousands of years have loved to hear us singing about that. But I noticed a strange musical trend in the late 1950s and early 1960s where there were tons of songs about teenagers dying. Some examples would be Mark

Dinning's Teen Angel, Leader of the Pack by the Shangri Laws, are two that come to mind. And I just thought to myself, oh, that's strange because I had the same perception that you do that popular songs are mostly about happy things. You know, these are things we want to dance to It's something you put on at a party. In what world would there be a trend about teenagers dying in car crashes and tons and tons of songs? So this was a trend, though, in the late 1950s and early 1960s, so much so that it had a name. They were called Teenage Tragedy Songs. And I started to explore that trend, and I wanted to write about it.

And ultimately, that set me off on a journey to write this book. And so what was that trend? Was it a trend, or was it just a coincidence? Or, I mean, that was the time when, you know, the late 50s, early 60s, when James Dean rebelled without a cause, teenagers had this reputation, this kind of bad boy reputation. Was that it? There are a couple things. I think the biggest contributor is the rise of the teenager, which sounds weird.

But before this period, there wasn't really the idea of your teenage years being a distinct period of your life. Of course, you were age 13 to 19 at some point, but for the most part, you were a child and then you were an adult. But starting in the early 20th century, compulsory education comes about, and now you have people in that age range stuck in school all day together, hanging out, and culture begins to emerge around them. And then ultimately, music companies, movie executives, decide to market things to those teenagers. At the same time, as you mentioned, there was something in the air. There are tons of tragedies in the first half of the 20th century between World Wars, the Great Depression, pandemics.

And at the same time, there were a bunch of really prominent stars who died very, very young. In music, you know, Buddy Holly comes to mind, but also in movies. I know you just mentioned James Dean. And when you put all that together, I think you get this very specific iteration of the teen tragedy song in that era. One of the things that always interests me is why some songs and some artists become hits and others don't in this sense. And you can see it like on American Idol. There are a ton of great singers in this world, and there's a ton of great songs in this world. But some just rise to the top, and maybe they all take different routes to get there.

But, you know, it isn't necessarily because they're great songs. singers, because there's probably, for every great singer, there's probably a better one. But I don't, I don't, I've never understood, like, or if you can explain how they got there. Ultimately, this is not just music, it is the music business. The goal is to sell records. And if you look at the history of pop of the music, in every generation, there's great music and there's bad music, but often the things that rise to the top of the charts are going along with contemporary trends of other songs and styles that are popular. And because of that,

you're going to have tons and tons of labels who are going to put out similar music at the same time. And there may be almost no reason for why one particular song or artist rises to the top in that moment. I think a good example of this is The Twist. In the early 1960s, a man named Hank Ballard put out a song called The Twist to, you know, it was somewhat popular. It's then covered by a singer named Chubby Checker, who is a quality singer, but this song ends up becoming massive. This song becomes so big that literally every other artist at the time released their own versions of the twist. And I just mean covers.

I mean related versions. Frank Sinatra had a song, a twist song. The Marvelettes, who had just topped the charts with Please Mr. Postman, decided to release a song called Twist in Postman. You see tons and tons of artists do this. And occasionally some of them will become popular. An artist named Joey D ends up topping the charts with a song called The Peppermint Twist. I won't go out and claim that Joey D. is the greatest musician of all time.

But in this moment, he managed to tap into the zeitgeist. And this is something we see again and again over the generations. There's a trend. A bunch of people try to hop on that trend. And occasionally you get lucky and you're the one who wins out. But it is certainly not predicated completely on talent. I think you have to have some degree of talent to get to the top of the charts. it is not always the most talented that make it there you know you would be the perfect person to ask about

this and that is one hit wonders it's a fascinating phenomenon where some people have one song it becomes a big hit and then we never hear from them again and sometimes they're really good songs and other people are able to crank out song after song after song and why the difference it's a very difficult thing to have any hit songs it's basically an impossibility to have multiple hit songs and to become a legend requires a combination of skill and luck that almost no one is blessed with so i always think when i think about one hit wonders i often think we think about them in a bad light or like oh you know they weren't good enough to have another honestly they were lucky enough to have one hit, which is more than 99.9% of musicians can say. But it is just very, very difficult

to stay on top for so long. I love that because you're right. We look at one hit wonder people as almost as a failure. Like you had your chance. Look, you were right there on top and you blew it when in fact, most people never get there. Are you able to look back at the history of popular music and point to a couple of songs that really either change the direction or turbo-boasted something, that were really big deals in the business. There are tons of hits that come to mind. I guess I can highlight a few. Of course, you could point to I want to hold your hand by the Beatles.

It really kicks off the British invasion. It makes a style of rock music popular. and the Beatles end up being tremendously influential. They didn't invent this, but the Beatles became so popular that if you wanted to be taken seriously after a certain point, you had to be writing and performing your own songs. That was not a completely new idea, but the Beatles really turbocharged that idea. In the 70s, this song called Rock Your Baby by George McCray comes to mind because it is sometimes called the first disco song.

I mean, you could argue about that, but if you think about it in the context of Disco, which was this revolutionary genre of music that was popular for about a decade, it's a genre that really turns many things on its head because the star in the disco community was the DJ, whereas previously the star in the music world was whoever was performing the song. But now someone that could make hits was a guy that was just spinning records. This was sort of a revolutionary idea. And I think Rock Your Baby by George McCray is a good example of. what was to come throughout the 1970s.

And I'll just give, I mean, like I said, there's tons of examples. One other that comes to mind is in 1991, there was a number one hit by a rap duo called PM Dawn, called Set Adrift on Memory Bliss. Some people might even call Set a Drift on Memory Bliss and PM Dawn a one hit Wonder. But the reason this song is important, it was the first number one hit under SoundScan, which was a new system that the billboards used to catalog the charts. Before that, the way it would work was Billboard would just call up a bunch of record stores and be like, hey, what's selling? Obviously, this is a legitimate way to create a list of popular songs, but it's also subject to human error and outright fraud.

What SoundScan did was if you were at the record store, once you bought your CD or whatever, when it was scanned, that data was sent immediately to Billboard. Overnight, the charts changed dramatically. Suddenly there was more alternative rock, hip-hop, and country. country on the charts. The first number one under this new paradigm was set a drift on memory bliss by PM Dawn. And I think it was, it signified ways that the record industry was biased before we got this more accurate data, but also what was to come. PM Dawn was a hip-hop duo and hip-hop became the dominant art form over the next couple of decades. We're talking about popular music and the business behind it. And my guest is Chris Dala Riva. He's author,

author of the book Uncharted Territory, what numbers tell us about the biggest hit songs and ourselves. Hi, I'm Adam Gidwitz, host of Grim, Grimmer, Grimmist. On every episode, we tell a grim fairy tale. Not the cute, sweet versions of the fairy tales that your children have heard so many times. No, we tell the real grim fairy tales. They're funny, they're weird, sometimes they're a little bit scary. But don't worry, we rate every episode grim, grimmer. or Grimmist, so you, your child, your family can choose the episode that's the right level of scary for you. Tune in to Grim, Grimmer, Grimmist, and our new season, available now. When they were young, the five members of an elite commando group nicknamed the Stone Wolves

raged against the oppressive rule of the Kradirakian Empire, which occupies and dominates most of the galaxies inhabited planets. The wolves fought for freedom, but they've been. failed, leaving countless corpses in their wake. Defeated and disillusioned, they hung up their guns and went their separate ways, all hoping to find some small bit of peace amidst a universe thick with violence and oppression. Four decades after their heyday, they each try to stay alive and eke out a living, but a friend from the past won't let them move on, and neither will their bitterest enemy. The Stone Wolves is season 11 of the Galactic Football League Science fiction series by author Scott Sigler.

Enjoy it as a standalone story or listen to the entire GFL series beginning with Season 1, The Rookie. Search for Scott Sigler, S-I-G-L-E-R, wherever you get your podcasts. So, Chris, back in the day when I was a rock-and-roll disc jockey, and before that, there weren't too many ways to have a hit record. I mean, you recorded a song, but you had to have a record label that had promotion people that would go out and promote the song to radio stations. Radio Airplay had a lot to do with how successful a song was going to be. There were gatekeepers that if

your stuff didn't match what they wanted it to sound like you would never get your record released. It's changed, but how has it changed? It's a whole new world and how things work. and the biggest thing that changed, in my opinion, is distribution costs. Back in the day, you really needed a record label because, all right, maybe you could get into a studio to record something, but how are you going to get this into not just a record store, but record stores all over your region, all over the country, all over the world for that matter, the costs were insurmountable for a small, independent artist. Jump forward to today, I can record a song.

bedroom, I can go on to a digital distributor like Distro Kids, a popular one, where it's like $20 for the year. I click upload and my music will be available on every streaming service you could possibly think of around the world. There are no gatekeepers to getting your music out there, to getting heard. The labels still have a ton of power because they own many relationships. And I think the way it typically works now is that back in the day, Clive Davis can discover Whitney Houston. She doesn't have an audience and he could be like, I'm going to make you a star. I'm going to get you on MTV. I'm going to get you on radio. Wouldn't always work. But Clive and his record label compatriots held the keys to the castle. Now you can build an audience for yourself online and then a record label will sort of come in at the 11th hour and be like, all right, we're going to give you a deal. We're going to pour gasoline on this fire. So if you want to be, you know, Taylor Swift or the biggest possible superstar, You still need the know-how of a label, but you can get your music out there, you can get it heard, and you can build a legitimate career without going through a label.

So we live in a completely different world than we did a few decades ago. And the people who put music out online and some people become stars as a result, but probably most people don't. So what's the difference? What is it? Is it the music is just so much better? or what is it that makes some online musicians successful? Another good question that if I had the answer to,

then you'd probably be interviewing me about my successful music career. But I think there are a couple things that we can point to that are different. A, because it's so easy, I mean, you certainly have more amateurs who are putting out music. And if you are talented, it's a little bit easier to cut through that noise. at the same time, it's never always been just about the music. And in this day and age, the easiest way for people to get attention is on social media. How, if at all, how is the technology by which music is delivered to people, which is so very different than it used to be?

How has that technology impacted the way the music is created in the first place? I think you often hear people talk about how songs have become shorter in the streaming age and there are incentives for that because the way streaming works is that you get paid after a 30 second stream and you get paid more if you command a bigger piece of the streaming pie so if you have a bunch of really short songs

you'll command a bigger piece of that pie you'll get paid out more and one thing I often think about is artists respond to incentives in that musical evolution is often downstream of technological innovation. What that means is that artists are responding to the incentives created by different technologies. And I bring up shorter songs because I think people do talk about that a lot, but something that I came across is actually song titles have gotten shorter too. And this may seem like a weird, small thing to bring up,

but I think it's a great example about how artists are influenced by the technology that they're interacting with. The reason that titles have become shorter, it was a trend that started in the early 2000s and then accelerated in the last decade. And think about how you listen to music now, probably on your phone. If your song title is too long, it's going to get cut off on the phone display. It seems artists want people to be able to see the entire title to their song. And because of that, they've shortened them so it can be seen. I don't know if any artist would acknowledge this if you spoke to them directly about it, but I think it's clear. again that artists respond

to technological incentives and we see this over and over throughout the decades. And this is one little example but I think it illustrates the trend really well. Another trend that I've noticed is how in commercials today they often use music from hit songs from the 60s or 70s

you'll hear the Rolling Stones or the Who song in a commercial today and I'm wondering if there's something about the music business that drives that because there's plenty of good music out today. Why go back that far and why those songs? Another very keen observation there, and that is a legitimate trend. I do actually think it's somewhat problematic. Part of the reason that that trend started was over the last decade or so, there's been a ton of money spent by labels and private equity firms

buying up the intellectual property rights to big hits of the 20th century and they've been spending a lot of money Bruce Springsteen's catalog went for 500 million apparently Dillon's went for 400 million I think only part of Michael Jackson's went for like a billion dollars that's a lot of money

and if you want to get your money's worth if you want to turn a profit on that you need to make people aware of these songs and you need to generate income streams for these songs. One way to do that is to get these songs synced in commercials. So there's a huge incentive for these investors to get these songs placed in commercials. At the same time, you see many, this affects many other trends. I was talking to someone

recently about a surge in music biopics over the last decade. Again, the Dylan and Springsteen ones come to mind, but there have been so many. There was a Whitney Houston one. There was a Bob Marley one. There wasn't Elvis Presley one. The reason this happens is you will, if you see a, a music biopic being made, you can often find that that musician's catalog was sold not long before that, and it is just the investor trying to turn a profit on that. And it's the same trend in movies as you see with commercials, but you are 100% right. Lastly, I wanted to ask you, because I think people wonder about this. Is writing songs and performing songs a great way to earn money for the rest of your life? Broadly, no. I would not recommend you pursue the career if you're looking

for riches. There are easier ways if you want to make a ton of money. There's a huge income disparity in the music field between people who are very successful and people who are, you know, in the middle class of songwriters and artists. But if you are lucky enough to write a single hit song and you don't spend too lavishly, I mean, you can never have to work a day again the rest of your life. The prime example I always think of is the Katrina and the wave song, I'm Walking on Sunshine, which gets licensed for commercials every year. It's in tons and tons of movies. It's still played on the radio regularly. In the last I'd heard in the 2000s, the guy who wrote the song from the band was making over a million dollars a year just from that song. So if

you're lucky enough to have one big hit, you are set for life. But that's, I guess we talked about earlier, that's very, very hard to do. Well, this was fun. It's obviously a subject I enjoy talking about, as do you, since you wrote a whole book about it, and it was very insightful. Chris Dalariva has been my guest, and the name of his book is Uncharted Territory, what numbers tell us about the biggest hit songs and ourselves. There's a link to that book in the show notes. Chris, great, great job, thanks. These were very unique questions, so I appreciate them. Have you ever wondered, why are we?

rainbows in the shape of a bow. Why do sunflower seeds, if you ever look at the seeds in the flower, why do they arrange themselves in such perfect spirals? Why are there some left-handed people, but not very many? The answers to questions like these become even more intriguing when you look at them through the lens of mathematics. Eddie Wu is here to show just how much of the world is shaped by math, but we hardly notice it. Eddie is the head mathematics teacher at Cherry Brook Technology High School in Sydney, Australia, and back in 2012, he began recording his lessons and posting them on YouTube, creating Woo-tube, and he now has more than 600,000 subscribers and over 33 million views. He's also author of a book called It's a Numberful World,

how math is hiding everywhere. Hi, Eddie, welcome to something you should know. Thanks for having me, Mike. So let's start with a rainbow, because every time you see a rainbow outside, it's always in the shape of a half circle, in the shape of a bow, but why that shape?

So I actually was very recently up in a plane. You can see that actually the shape of a rainbow is not just sort of half of a circle. It is actually a full circle. And what is happening here is one of these most phenomenal ideas that I've ever experienced, which is that I want you to picture, Mike, the rain has just been falling for the last couple of hours, but suddenly it's stopped. The clouds are starting to part, and the sun is beginning to shine again.

All right, what is happening in this moment? Well, firstly, even though the rain has stopped, there is actually still a lot of water in the air. All of these hundreds of millions of droplets kind of still suspended in the atmosphere. sphere. And each one of those individually acts like a little prism and a little mirror that reflects light from the sun around all of the different directions. So every one of those hundreds of millions of raindrops in the air is doing that. It's refracting the light into its different component colors. But a raindrop is not a triangular shape. It's round. And so what will happen is that light will refract, but it will rebound on the inside.

of that roughly spherical raindrop and it will go back, it will reflect back in the direction roughly that it came from. Now, there are some of those raindrops in the air out of those countless number that will reflect back to your eyes and to mine that particular spectrum

and all of those particular raindrops are going to be in the shape of a cone. Now, if you look at a cone from the top, you don't see the whole sort of, you know, ice cream cone shape. You actually see the cross section of a crows. which is a circle. And that circle is the shape of the rainbow that you and I see. It's just that we usually only see half of it because the horizon is blocking its path. But this unlocks one of

those beautiful things about rainbows, which is that if you and I, Mike, were standing right next to each other, we would both look up and see a rainbow in the sky, but we'd both be seeing different rainbows because you see a different set of raindrops to me. So help me understand this concept in science and math. that everything wants to be the same temperature as everything around it, which I think most of us have experienced. It's why ice melts in a warm room and why ice freezes outside when it's really cold.

Things want to be the temperature of everything around it. So Newton was one of the first people. Sir Isaac Newton explored this law of cooling, which is that, as you mentioned, temperature, which is really the measurement of heat energy, which is every little atom around you vibrating at a different frequency, that's an amount of energy that wants to be shared, it wants to be diffused throughout a zone.

Now, the reason why that's mathematics is because we can use that diffusion of heat in a very predictable way to know things like, for example, crime scene investigators. When they want to know the exact time of death of a victim, they can say, well, we actually know what temperature a human body is when it's alive, and it will very predictably drop off at a certain rate so that if we measure the temperature of that body, we can actually, with a great degree

of accuracy, no, if this happened within a certain number of hours, we can even pin down the time of death. So to me, this very predictable mathematical model, it's called exponential decay, starts off very steep and the temperature drops rapidly, and then it sort of levels out and becomes this sort of gradual curve. This is a mathematical idea that we can use to, again, interpret and understand the world around us. Again, you don't need to know the formal mathematics to intuitively get that. When you brew a cup of coffee or pop in a cup of tea, it quickly goes from maximum temperature, boiling, steaming down to a temperature that's actually one you can drink.

And then, of course, it drops further and becomes a little bit uncomfortable and you probably want to warm it up again. So this idea is very intuitive to all of us. And that's because it's a mathematical pattern that we experience over and over again, and our brains, our minds are attuned to. So when you pour coffee into the cup, the coffee wants to assume the temperature of the cup and the cup wants to assume the temperature of the coffee? A hundred percent, Mike. And one of the things I used to imagine as a kid is this invisible bucket brigade.

I don't know if you've got this picture in your mind of all these different people, sort of passing water one to another using a string of buckets, well, that's exactly what atoms are doing. They're each vibrating one another and passing that heat energy along the way until it is evenly spread throughout the environment, which is why, of course, if you come to that cup of coffee after an hour, it will be exactly the same temperature as the surrounding environment, which is probably not very pleasant to drink. So one of these mathematical formula things that I find really interesting is, I've heard. this explanation before but I can't I can't recall it like when you have a lot of

people in a room the chances of people sharing the same birthday how that works if you just have 23 people in a room there is a 50% chance that two of those people are going to share the same birthday which sounds ridiculous but it actually is true and we can prove it mathematically in the same way that we were doing that compound interest explanation before. Every additional person that you add has more possible connections with every other person in the group. And to make sure that no one has the same birthday, actually there are fewer and fewer days that are possible. And when you go ahead and you do the probability calculation, it ends up, I think it's 50.06% when there is 23 people

in the room. And that seems extremely surprising, but the mathematics bears it out. And I think That's one of the things that's most powerful about mathematics. We have this intuition for how the natural world works. But sometimes we're surprised by things, and mathematics can help us to actually use clear logic and deduction to see what's really true. Well, wait a minute, because, of course, people would think there's 365 days in a year. So the chances of you and me having the same birthday would be one in 365. how could it possibly be one out of 20 or a 50% chance of one out of 23? Yes. So again, I know this is very counterintuitive, but let's think about it from the opposite point of view.

This is something that mathematicians call the complement. So the probability that we don't share the same birthday is 364 out of 365, which again seems like an extremely high chance. It's more than 99% right. So, of course, it's unlikely that we would share the same birthday. There's more than a 99% chance. We've got different ones. But when we add the next person in, we're not multiplying by 364 divided by 365. There are a few options. You and I, we occupy two of the birthdays. So now it's going to be 363 out of 365.

And then the next person who comes along, 362. Now, again, those fractions don't seem like they're going to be very small, very fast. but the more of them that are multiplied together. And the thing is, we don't often multiply 23 numbers one after another after another. So our intuition for how big or small that number is going to be turns out to be quite poor. But by the time you get to the 23rd person, all of those fractions reduce that number down and you end up having a chance less than 50% that we all have different birthdays. So therefore, the chance that at least one person shares a birthday with another ends up being more than 50%.

50%. Again, counterintuitive and surprising. So it's not that if 23 people were to walk into this room, that there's a 50 chance that one of them shares my birthday. It's that one of all of us share a birthday. Yes, exactly right. And that's part of the counterintuitive part of it. We have a bias to think about it from our own point of view. And you're right. If it's just me and those other 22 people or yourself, then of course, the chance is much higher that I'm not going to share birthday with any of them. What's the math of sunflowers? The beauty of the sunflower, the mathematical genius of it, really only comes when you zoom in nice and close. So if anyone gets to go into a nursery,

a plant nursery, or if they have some sunflowers growing near them, or even if you just want to go on the internet and search for a picture, do a close-up of the pattern of seeds that's on the face of a sunflower. And one of the things you'll recognize is it isn't just this dark, flat area that's surrounded by beautiful golden petals. Actually, there are tens, dozens, hundreds of individual seeds that are there all nestled together. But this is the key part. They are not arranged randomly, Mike. They are arranged in a beautiful geometric pattern that actually relates to something called the golden ratio. And it's a number, it's about 1.618, roughly, that's been used in architecture. Some people have found it in all kinds of places in nature. And the seeds,

the florets of a sunflower are all spaced out in the golden ratio of an angle, what's called the golden angle. And that's what gives it this very particular geometry that we all recognize it is wonderfully orderly in the way that it's arranged. And it actually is, is a similar kind of pattern that many plants use to space out their leaves to make sure that one leaf doesn't shade another one. And this becomes even more challenging when you've got three or four or five or 500 leaves.

And so this spacing out using the golden angle and the golden ratio is what number one enables the plant to be efficient with its photosynthesis. And number two allows the sunflower to space out its seeds and florets in this beautiful and very predictable geometry. So it's not as though the sunflower is thinking of doing this, but evolution has shown that the sunflowers that did this were the most productives.

And that's why those are the ones that have survived and have gone through survival of the fittest and been the ones that we see today. Can you explain the math of randomness in a way that people could grasp? The mathematics of randomness is an amazingly broad field. So probably the place that I would go to is the idea of, If you are flipping a coin repeatedly, we know that there's equal likelihood that it's going to come up heads or come up tails. And that equal likelihood means random. That's the whole idea

that one outcome is not more likely than the other. But one of the things that's most amazing in the study of randomness is that randomness cannot help but give rise to appearance of order. So, for example, if you didn't flip one coin, if you flipped a thousand coins and you laid them all out in order. What would happen is that there is an extremely high likelihood that somewhere in your 1,000 coins, you would have a string of tails, tail, tail, tail, tail, tail, as you were going along. You might get 10 or 15 tails in a row, which sounds like it isn't very random, but actually is almost guaranteed to happen if you are going to flip that number of coins in a row. Now, this is really dangerous. People might have

If they're interested in sport, they might have heard of the hot hand, or if there are people who have taken a trip to a casino and just gone there to entertain themselves, you might have heard of the gambler's fallacy, which is this idea that, oh, I haven't won many turns on this game. Surely the next time I'm going to win. Well, the mathematics of randomness tells us that even though it's tempting to believe that after losing 10 times, I'm likely to win the next time. If it's an equally likely outcome, if we went to the roulette wheel and we spun the ball around, it's going to be an equal likelihood every single time. It doesn't matter. The roulette wheel doesn't care that you just lost 10 times. It's going to start again. And the

chance of winning each time is, unfortunately, pretty low. And that's why casinos make so much money. So the mathematics of randomness is about being able to say, all right, even though I can't necessarily know what's going to happen next, I can expect some order to flow out of that, and quite famously, even random things in a population, like say, for instance, the exact height of an individual. When they're born, you can't know how tall they're going to be. You can guess based on how tall their parents are, that genetic material goes together in a mix. You can't know for certain. However, over a large population, just like with the 1,000 coins, there is order that emerges. We get this predictable shape called the normal.

distribution, more familiar to people as a bell curve. So that randomness, the technical name is stochasticity, gives rise to order and predictability. And that's why we can do things like predict the weather, even when there is some randomness involved. So left-handedness is a topic I'm interested in because I'm left-handed. And, you know, it's not the worst thing in the world to be left-handed, but it is inconvenient sometimes and difficult sometimes because we live in a right-handed world. And I've read that left-handed people have a shorter life expectancy primarily due to industrial accidents and accidents with tools and things that are made for right-handed people that left-handed people have to use. But it makes you wonder why left-handed people

aren't evolved out. You know, there's like no reason. I mean, I'm glad they're not. But why have them. Left-handedness is an unusual trait. By definition, I mean, you will probably know a left-hander, but if you were to just bump into someone on the street and ask them which hand they write with or which hand they play sport with, they are mostly likely to say they're right hand. It's roughly 90% of the population that has this right-handedness to them. But the reason why left-handedness exists is because by virtue of its infrequency, the fact that it's a bit out of the ordinary, it actually infers a certain advantage onto the people who have that property. If you think about the fact that, say, for instance, there are members of my family

who are very avid sports followers. And in sport, when you hold a racket or a bat with your left hand, or perhaps if you're a boxer, if your dominant hand of side is your left side, that makes you a little bit unusual. So when you get on the tennis court, you're used to playing shots in a certain way to favor playing against the right-hander because most of the people you play against are right-handers. But if you meet a left-hander, you hit a shot to what you think is their weak side, but actually, it's their strong side and they can hit it back. They can hit a winner very confidently, very easily, and suddenly you're in trouble. Now, on the tennis court, that's just a matter of winning or losing a game. But earlier on, in our evolutionary background,

that left-handedness would probably have inferred on you an advantage of survival. You know, when we talk about survival of the fittest out in the natural world, is those people who are stronger, who maybe have to show their dominance and have to be, you know, able to fight off other people who want to lead the tribe or things like that, that ability to be something uncommon or unusual to your opponent. And in this case, being left-handed is actually an evolutionary advantage. But here's the thing, you might say, well, hold on a second. When something has an evolutionary advantage, it's going to become more and more common.

But let's imagine if we go forward tens of thousands or hundreds of years, you would then have lots and lots of left-handers in the population. That means that they become more common and their advantage disappears because you're meeting left-handers all the time and you're pretty familiar with the strengths and weaknesses that they have. So in that way, if there were lots of left-handers in the population, they would very naturally decrease again. And we would come back to what we call this equilibrium. So that is part of why left-handedness exists. Ultimately, the genes are still a bit of a mystery to us. But that hypothesis, that mathematical way of thinking about it, is extremely powerful. Since we're having this conversation in the winter, let's talk about the math of snowflakes.

One of the most famous facts about snow is that every individual snow number one, it's unique. It's like a fingerprint. But number two, if you look at a snowflake underneath a microscope, it has this beautiful hexagonal symmetry to it. And I've often wondered why. And really the reason is that every individual water molecule has one oxygen and two hydrogens. And they fit around it at a particular angle that when you fit them together and you make them very cold and they crystallize, you end up having this interlocking shape, a bit like a jigsaw puzzle, except each water molecule can fit onto exactly five others. And you get a hexagon, which ends up being the center, the base, the nucleation site of

that snowflake. And so every snowflake begins with a hexagon, and as other water molecules grab on in the air and join the party, they form outwards in this symmetrical, beautiful shape. So again, it's microscopic. You almost wouldn't believe that it's there, but mathematics is the engine that makes our entire world run. Well, it's always fun to look at life, different parts of our lives, through the lens of math, because often the explanation is so surprising.

I've been talking to Eddie Wu. He is the head math teacher at Cherry Brook Technology High School in Sydney. He is the creator of Woo Tube, that's W-O-O-O-T-U-E on YouTube, and he has over 600,000 subscribers. And his book is called It's a Numberful World, How Math is Hiding Everywhere. And there's a link to that book in the show notes. Thanks, Eddie. No, the pleasure is all mine, Mike. Thank you so much for letting me have the opportunity to speak with your audience.

So in the workplace, there are 12 basic skills. You're likely excellent at a few of them, mediocre at several of them, and really bad at a couple of them. So let's see if you can identify your weakest ones. Here are the 12 skills. Self-restraint, working memory, emotion control, focus, task initiation, planning and prioritization, organization, time management, defining and achieving goals, flexibility, observation, and stress tolerance. And you may want to hit that little rewind thing and play that list back, because here's why it's important to identify your weakest ones. They're not very changeable.

Yes, you can improve on them, but if you're really bad at some of these skills, it's going to be very hard to get good at them. So they should not be part of your job description. Instead, your job should include the two or three skills that you're really great at. Interestingly, in a survey of 2,000 workers, the majority of people said their job did not play to their strengths. This is all according to Chuck Martin, who, wrote a book called Smarts. And that is something you should know. I certainly, I really do

appreciate the fact that you take time to listen to this podcast. It means a lot. And if you would like to share it with someone you know, that would mean a lot too. I'm Mike Carruthers. Thanks for listening today to Something You Should Know. The Infinite Monkey Cage returns imminently. I am Robert Ince and I'm sat next to Brian Cox who has so much to tell you about what's on the new series. primarily eels and what else that it was fascinating though the eels but we're not just doing eels are we're doing a bit with brain computer interfaces timekeeping fusion monkey business cloud signs of the north pole and eels did i mention the eels is this ever since you bought that timeshare underneath the sagas OC listen on bbc.com or wherever you get your podcasts