← Something You Should Know
Something You Should Know
What Makes a Hit Song & Why You Never See the Same Rainbow Twice
00:47:58
Why songs become hits, why rainbows curve, which workplace skills matter most, and how to recover from a bad night’s sleep
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- [00:02]
Mike Carruthers
When the holidays start to feel a.
- [00:03]
Host
Bit repetitive, reach for a Sprite Winter.
- [00:06]
Mike Carruthers
Spiced Cranberry and put your twist on tradition.
- [00:11]
Host
A bold cranberry and winter spice flavor Fusion Sprite Winter Spice Cranberry is a refreshing way to shake things up this.
- [00:18]
Mike Carruthers
Sipping season, and only for a limited time.
- [00:21]
Host
Sprite Obey your thirst. 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.
- [00:39]
Mike Carruthers
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.
- [00:52]
Host
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.
- [01:05]
Eddie Wu
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.
- [01:20]
Host
All this today on something you should know. So I don't know if you do this, but every January I get this burst of motivation like, okay, this is the year I finally start that business idea. And then, well, you know, February shows up and nothing happened. So if you've ever thought, well, maybe I should just start already, this might actually help you do it this time. Because 2026 really can be the year that you launch your business. The year you become the entrepreneur or the founder that you've always been imagining. And honestly, the move that makes it real is starting with with Shopify. Now, maybe you've had an idea sitting around forever, or maybe people keep telling you you should sell that thing you make. Well, with Shopify, 2026 is the year you actually do it. Shopify gives you everything you need to sell online and in person. Millions of entrepreneurs, from big brands to total beginners, already made the leap. You can build your store really fast with hundreds of templates that you can customize. And setup is easier with Shopify's built in tools that write product descriptions and headlines and helps you edit photos. All those detaily things that tend to paralyze me. Marketing's built in too. Email campaigns, social media campaigns, all from the same dashboard. In 2026, stop waiting and start selling with Shopify. Sign up for your $1 per month trial and start selling today at shopify.com sysk go to shopify.com sy that's shopify.com sysk hear your first this new year with Shopify by your side. Something you should know Fascinating intel, the world's top experts and practical advice you.
- [03:20]
Mike Carruthers
Can use in your life today.
- [03:23]
Host
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 weekends? 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 youg 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 to it's changed the music itself in surprising and profound ways. Chris Dalla Riva 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 youg Should know, thanks for having me.
- [06:00]
Mike Carruthers
I'm really happy to be here.
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Host
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?
- [06:20]
Mike Carruthers
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 Denning'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 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 that I wanted to write about it, and ultimately that set me off on a journey to write this book.
- [07:28]
Host
And so what was that trend? Was it a trend or was it just a coincidence or. I mean, that was the time when the late 50s, early 60s were. When James Dean rebelled without a cause. Teenagers had this reputation, this kind of bad boy reputation. Was that it?
- [07:48]
Mike Carruthers
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, 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.
- [08:58]
Host
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, a high or if you can explain how they got there.
- [09:38]
Mike Carruthers
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 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, was. 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 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 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. But it is not always the most talented that make it there.
- [11:28]
Host
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?
- [11:52]
Mike Carruthers
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.
- [12:31]
Host
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?
- [13:05]
Mike Carruthers
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 want it 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 youk Baby by George McCrae comes to mind because it's 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 youk 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 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, 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 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.
- [15:42]
Host
We're talking about popular music and the business behind it. And my guest is Chris Dallariva. He's author of the book Unchartered Territory. What numbers tell us about the biggest hit songs and ourselves. It's a busy time, cold weather, holiday plans. It's the time of year when I just want my wardrobe to work without any effort. Which is why I've been all about quints. They make it easy to look sharp, feel good, and find gifts that actually last. Everything they sell is made from premium materials, built to hold up and priced without the luxury markup Quince makes the essentials everyone needs. Their Mongolian cashmere sweaters, of which I have more than one, are just 50 bucks and honestly, they feel like something triple the price. Their Italian wool coats look and feel designer and their outerwear lineup is really solid. Down jackets, wool top coats, and even leather styles that are made to last season after season. Everything at Quint's is made from premium materials in ethical, highly trusted factories. And because Quince cuts out the middlemen, you get the same quality as luxury brands at a fraction of the cost. Seems like everyone I know is now shopping at Quince. You should probably too get your wardrobe sorted and your gift list handled with Quince. Don't wait. Go to quints.com sysk for free shipping on your order and 365 day return. Now available in Canada too. That's Q-U-I-N-C-E.com sysk free shipping and 365 day returns. Quince.com sysk ever notice how half your day isn't spent doing the work, it's organizing the work. Notes, links, ideas scattered everywhere. You start with good intentions, but by midday you're buried under the admin side of creativity. That's why I've been using Notion Agent. It's like having a digital version of me that actually gets things done. Notion becomes your AI teammate and brings all your notes and docs and projects into one connected space that just works. It's seamless, flexible, powerful, and it's actually fun to use. With AI built right in, you spend less time switching between tools and more time creating great work. And now with Notion Agent, your AI doesn't just help with work, it finishes it. I've used it to organize podcast prep. It finds notes and tags guests and even drafts summaries of old episodes so I can focus on what really matters, the conversation. Notion Agent can do anything you can do in Notion. It taps into your workspace, the web, even tools like Slack and Google Drive to complete actions end to end. When my Notion Agent is running, my brain feels lighter. It's like finally having space to think again. Try Notion now with notion agent@notion.com something that's all lowercase letters notion.com something to try your new AI teammate notion agent today. And when you use our link, you're supporting our show notion.com something 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 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?
- [19:56]
Mike Carruthers
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 Distrokids, 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 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 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.
- [21:41]
Host
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?
- [22:01]
Mike Carruthers
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. 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.
- [22:32]
Host
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?
- [22:47]
Mike Carruthers
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 32nd 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 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. 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.
- [24:28]
Host
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, 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?
- [24:56]
Mike Carruthers
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 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. But 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 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.
- [26:27]
Host
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?
- [26:42]
Mike Carruthers
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 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.
- [27:37]
Host
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 Terr. 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.
- [27:59]
Mike Carruthers
These were very unique questions, so I appreciate them.
- [28:03]
Host
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- [29:42]
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- [30:20]
Host
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 Cherrybrook Technology High School in Sydney, Australia. And back in 2012, he began recording his lessons and posting them on YouTube, creating WooTube. 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 how math is hiding everywhere. Hi Eddie, welcome to something you should know.
- [31:23]
Eddie Wu
Thanks for having me, Mike.
- [31:24]
Host
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?
- [31:35]
Eddie Wu
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 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. 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 and 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.
- [33:42]
Host
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.
- [34:07]
Eddie Wu
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, 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. And 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.
- [35:51]
Host
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.
- [36:01]
Eddie Wu
100%, 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.
- [36:34]
Host
So one of these mathematical formula things that I find really interesting is I've heard this explanation before, but 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.
- [36:53]
Eddie Wu
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.
- [37:53]
Host
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 1 in 365. How could it possibly be 1 out of 20? Or a 50% chance of 1 out of 23?
- [38:12]
Eddie Wu
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 fewer 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 1 after another, after another. So 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%. Again, counterintuitive and surprising.
- [39:33]
Host
So it's not that if 23 people were to walk into this room that there's a 50, 50 chance that one of them shares my birthday, it's that one of all of us share a birthday.
- [39:45]
Eddie Wu
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 a birthday with any of them.
- [40:00]
Host
What's the math of sunflowers?
- [40:04]
Eddie Wu
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 a similar kind of pattern that many plants use to space out their leaves to make sure that one leaf doesn't show 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 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.
- [42:06]
Host
Can you explain the math of randomness in a way that that people could grasp?
- [42:13]
Eddie Wu
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 1,000 coins and you laid them all out in order, what would happen is that there is an extremely high likelihood that somewhere in your 1000 coins, you would have a string of tails, 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 heard, 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, you know, 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 they're 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 1000 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.
- [45:02]
Host
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 is like no reason. I mean, I'm glad they're not, but why have them?
- [45:43]
Eddie Wu
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 play sport with, they are mostly likely to say their 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 you, your dominant hand or 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 survive 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 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. 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.
- [48:20]
Host
Since we're having this conversation in the winter, let's talk about the math of snowflakes.
- [48:26]
Eddie Wu
One of the most famous facts about snow is that every individual snowflake, number one, is, 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 side 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 shade. 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.
- [49:30]
Host
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 Cherrybrook Technology High School in Sydney. He is the creator of WooTube. That's w o o t u b e on YouTube, Eddie. And he has over 600,000 subscribers. And his book is called It's a Numberful How Math is Hiding Everywhere. And there's a link to that book in the show notes. Thanks, Eddie.
- [50:03]
Eddie Wu
No, the pleasure is all mine, Mike. Thank you so much for letting me have the opportunity to speak with your audience.
- [50:11]
Host
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 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 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. Limu Imu and Doug Here we have the Limu Emu in its natural habitat, helping people customize their car insurance and save hundreds with Liberty Mutual. Fascinating. It's accompanied by his natural ally, Doug.
- [52:07]
Eddie Wu
Uh, Limu is that guy with the binoculars watching us.
- [52:10]
Host
Cut the camera. They see us. Only pay for what you need@liberty mutual.com Liberty Liberty Liberty Liberty Savings Ferry Unwritten.
- [52:17]
Mike Carruthers
By Liberty Mutual Insurance Company and affiliates.
- [52:19]
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