What Makes a Hit Song & Why You Never See the Same Rainbow Twice

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

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:02Mike Carruthers?

  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?

• 0:14Speaker 01

  Actually, song titles have gotten shorter. If your song title's 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.

• 0:27Mike Carruthers?

  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.

• 0:40Speaker 02

  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.

• 0:56Mike Carruthers?

  All this today on Something You Should Know. Now, here's something that might be worth a minute of your time. How would you like $1,000 to spend on shopping? Especially with the holidays coming. Well, the people behind Shopify have a shopping site called shop.com. And to celebrate the new shop.com, they're giving away $1 million in Shop Cash. But not to one person. A thousand people will each win $1,000 in Shop Cash. And shop.com is actually a really clever idea. It brings lots of different stores together in one place.

• 1:39Mike Carruthers?

  So, instead of bouncing around from website to website, you can search across stores, find what you're looking for, and track your orders, all in one place. Clothes, electronics, gifts, things for the house, all kinds of stuff. And whether you win or not, it's worth knowing. But with 1,000 chances to win $1,000, I'd certainly take a look. Enter to win the $1 million Shop Cash giveaway from now until November 1st. Just go to shop.com. There are so many ways to win. That's shop.com. Shopping designed around you. No purchase necessary. Restrictions apply. Official rules available at shop.com.

• 2:26Speaker 03

  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.

• 2:40Mike 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.

• 3:25Mike Carruthers?

  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.

• 3:55Mike Carruthers?

  Popular music is often called "the soundtrack of our lives." And it sounds a little cliché, but cliché 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

• 4:39Mike Carruthers?

  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 Audiomac. 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.

• 5:11Speaker 01

  Thanks for having me, I'm really happy to be here.

• 5:14Mike Carruthers?

  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?

• 5:32Speaker 01

  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 Las 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...

• 6:16Speaker 01

  Happy things, you know, these are the 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 that I wanted to write about it. And ultimately, that set me off on a journey to write this book.

• 6:40Mike Carruthers?

  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?

• 6:59Speaker 01

  There are a couple of 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 aged 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.

• 7:42Speaker 01

  At the same time, as you mentioned, there was something in the air. There are tons and 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.

• 8:09Mike Carruthers?

  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 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 how, or if you can explain how they got there.

• 8:50Speaker 01

  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 popular 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 gonna have tons and tons of labels who are gonna 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.

• 9:36Speaker 01

  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 don't 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 Twistin' 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.

• 10:20Speaker 01

  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, but it is not always the most talented that make it there.

• 10:41Mike Carruthers?

  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?

• 11:05Speaker 01

  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.

• 11:44Mike Carruthers?

  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 changed the direction or turbo-boosted something? That were really big deals in the business?

• 12:17Speaker 01

  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 McCrae comes to mind because it's sometimes called the first disco song. I mean, you could argue about that.

• 12:59Speaker 01

  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 McCrae. 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,

• 13:43Speaker 01

  called Set Adrift on Memory Bliss. Some people would, might even call Set Adrift 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 Billboard 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.

• 14:27Speaker 01

  Suddenly, there was more alternative rock, hip-hop, and country on the charts. The first number one under this new paradigm was Set Adrift 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.

• 14:54Mike Carruthers?

  We're talking about popular music and the business behind it. And my guest is Chris Dalariva. He's author of the book Uncharted Territory: What Numbers Tell Us About the Biggest Hit Songs and Ourselves. So Chris, back in the day, when I was a rock and roll disc jockey, and before that, I mean, 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,

• 15:38Mike Carruthers?

  you would never get your record released. It's changed, but how has it changed?

• 15:45Speaker 01

  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 in my bedroom. I can go onto a digital distributor like DistroKid's a popular one, where it's like $20 for the year.

• 16:25Speaker 01

  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 gonna make you a star. I'm gonna get you on MTV. I'm gonna 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 gonna give you a deal.

• 17:10Speaker 01

  We're gonna 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.

• 17:30Mike Carruthers?

  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?

• 17:49Speaker 01

  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 of 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, 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.

• 18:20Mike Carruthers?

  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?

• 18:35Speaker 01

  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, and that musical evolution is often downstream of technological innovation. What that means is that artists are responding to the incentives

• 19:16Speaker 01

  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 title, 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.

• 20:01Speaker 01

  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.

• 20:16Mike Carruthers?

  Another trend that I've noticed is how in commercials today, they often use music from, you know, hit songs from the 60s or 70s. You'll hear, you know, 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, you know, there's plenty of good music out today. Why go back that far and why those songs?

• 20:44Speaker 01

  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, you know, Bruce Springsteen's catalog went for 500 million. Apparently Dylan'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

• 21:29Speaker 01

  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 was an Elvis Presley one. The reason this happens is you will, if you see a... A bi- 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

• 22:09Speaker 01

  on that. And it's the same trend in movies as you see with commercials, but you are 100% right.

• 22:16Mike Carruthers?

  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?

• 22:30Speaker 01

  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 could never have to work a day again the rest of your life. The prime example I always think of is the Katrina in 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

• 23:14Speaker 01

  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.

• 23:25Mike Carruthers?

  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.

• 23:47Speaker 01

  These were very unique questions, so I appreciate, I appreciate them.

• 23:54Mike Carruthers?

  Have you ever wondered, why are 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,

• 24:36Mike Carruthers?

  he began recording his lessons and posting them on YouTube, creating WuTube. 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.

• 24:57Speaker 02

  Thanks for having me, Mike.

• 24:58Mike Carruthers?

  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?

• 25:09Speaker 02

  So I actually was very recently up in a plane. You can see that actually, the shape of a rainbow is not just, you know, 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.

• 25:50Speaker 02

  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... 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

• 26:31Speaker 02

  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 cone, 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.

• 27:16Mike Carruthers?

  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.

• 27:40Speaker 02

  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.

• 28:24Speaker 02

  So if we measure the temperature of that body, we can actually with a great degree of accuracy know 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

• 29:05Speaker 02

  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.

• 29:25Mike Carruthers?

  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?

• 29:35Speaker 02

  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.

• 30:07Mike Carruthers?

  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. When you have a lot of people in a room, the chances of people sharing the same birthday, how that works?

• 30:27Speaker 02

  If you just have twenty-three people in a room, there is a fifty percent 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 fifty point zero six percent when there is twenty-three people in the room. And that seems extremely surprising, but the mathematics bears it out.

• 31:12Speaker 02

  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.

• 31:26Mike Carruthers?

  Well, wait a minute, because of course, people would think there's three hundred and sixty-five days in a year. So the chances of you and me having the same birthday would be one in three hundred and sixty-five. How could it possibly be one out of twenty or a fifty percent chance of one out of twenty-three?

• 31:46Speaker 02

  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 three hundred and sixty-four out of three hundred and sixty-five, which again, seems like an extremely high chance. It's more than ninety-nine percent, right? So of course, it's unlikely that we would share the same birthday. There's more than a ninety-nine percent chance we've got different ones. But when we add the next person in, we're not multiplying by three hundred and sixty-four divided by three hundred and sixty-five. There are fewer options. You and I, we occupy two of the birthdays. So now it's going to be three hundred and sixty-three out of three hundred and sixty-five. And then the next person who comes along, three hundred and sixty-two.

• 32:29Speaker 02

  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 We don't often multiply twenty three 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 twenty third person, all of those fractions reduce that number down. And you end up having a chance less than fifty percent 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 fifty percent. Again, counterintuitive and surprising.

• 33:06Mike Carruthers?

  So it's not that if twenty three people were to walk into this room, that there's a fifty fifty chance that one of them shares my birthday. It's that one of all of us share a birthday.

• 33:18Speaker 02

  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 twenty twenty two people or yourself, then of course, the chance is much higher that I'm not going to share a birthday with any of them.

• 33:34Mike Carruthers?

  What's the math of sunflowers?

• 33:37Speaker 02

  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.

• 34:21Speaker 02

  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 one point six one eight 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 a similar kind of pattern that many plants use that to space out their leaves to make sure that one leaf doesn't shade another one.

• 35:03Speaker 02

  And this becomes even more challenging when you've got three or four or five or five hundred 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 productive. 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.

• 35:40Mike Carruthers?

  Can you explain the math of randomness in a way that that people could grasp?

• 35:47Speaker 02

  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

• 36:32Speaker 02

  that somewhere in your one thousand coins, you would have a string of tails. Tail, tail, tail, tail, as you were going along. You might get ten or fifteen 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 heard if they're interested in sport, they might have heard of. Hot hand or if there are people who have taken a trip to a casino and you know just gone there to entertain themselves. You might have heard of the gambler's fallacy, which is this idea that, oh, I I haven't won many turns on this game.

• 37:12Speaker 02

  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 ten times, I'm likely to win the next time. If it's an equally likely outcome, if we went to the roulette 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 ten 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.

• 37:55Speaker 02

  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 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 one thousand 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.

• 38:36Mike Carruthers?

  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 the 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 there there's like no rea- I mean, I'm glad they're not, but but why why have them?

• 39:17Speaker 02

  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 their right hand. It's roughly ninety percent 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 on to 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

• 40:02Speaker 02

  your left hand, or perhaps if you're a boxer, if you, your dominant hand 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 favour 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.

• 40:46Speaker 02

  You know, when we talk about survival of the fittest out in the natural world, it 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 and 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.

• 41:28Speaker 02

  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.

• 41:54Mike Carruthers?

  Since we're having this conversation in the winter, let's talk about the math of snowflakes.

• 42:00Speaker 02

  One of the most famous facts about snow is that every individual snowflake, 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.

• 42:44Speaker 02

  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.

• 43:04Mike Carruthers?

  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 WooTube, that's W-O-O-T-U-B-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.

• 43:37Speaker 02

  No, the pleasure is all mine, Mike. Thank you so much for letting me have the opportunity to speak with your audience.

• 43:45Mike Carruthers?

  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

• 44:28Mike Carruthers?

  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.

• 45:13Mike Carruthers?

  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.