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[Assistant] Were you already like incorporating math content into, or were you going along completely as a guy who could be a comedian or anything?


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[Assistant] That first gig you mentioned, tell me the story of that because that must've been like your first teaching lesson as well.


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[Assistant] Did you have a level of confidence and persistence that this was going to happen or do you think if that night and that had tanked and things had gone badly at the start it might have all?


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[Assistant] Jumping forward a bit, you've now got, you know, Festival of Spoken Nerd and all the different things you do on YouTube and...


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[Assistant] You do a million different things and it's almost like this huge empire now. Was this the vision? Are you now living what you thought back then or were you thinking you'd just be like a comedian who goes to comedy clubs and maybe will one day get on TV? Or is what you're doing now what you were aiming for?


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[Assistant] How much are you driven by just like being a show off and wanting to be funny and make people laugh and the buzz that that gives you? And how much is there this kind of altruistic mathematics, the world must know the importance of, you know, which is driving you?


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[Assistant] Are you suggesting there are things, opportunities that you would not take because of the stand you're taking? Are there like things that have come to your head or have been offered to you that you've said no, because you want me to dumb it down too much or?


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[Assistant] You do perform live in front of pretty big audiences in the scheme of things, but obviously those audiences aren't as big as say the people who watch the YouTube videos that you're in.


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[Assistant] How do you compare the satisfaction or the thrill you get from doing like a live show with real human beings laughing out loud and you can smell them and you can hear them and that to a YouTube video you make that might have two or three million views, but it's surreal.


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[Assistant] Like the stakes are higher for some reason in our heads when there are other living human beings in the same room as us. Isn't that crazy? Because I will talk to people saying, can you help make a number five video for me? And they say, I can't possibly help you make a number five video. I've got to give a talk next week to 50 people and I have to spend a week preparing that talk. And part of me wants to say to them,


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[Assistant] Are you insane? Like if you do a video with me, a million people are going to watch. Have you run the numbers? Yeah, but yeah, I'm exactly the same. If I was giving a talk to 50 people next week, it's all I'd be really focused. Yeah. So it is, that's just our humanness, isn't it? So speaking of modes of communication, let's talk about books. You're just about to release your second.


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[Assistant] So the first one. Yep. Things to make and do in the fourth dimension. In which you misspelled my name.


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[Assistant] I'm not just saying this, Matt. I honestly really like the look of this book. It's nice, isn't it? I like the cover. That is because I'm a bit of a plane aficionado and the front of the book is a plane.


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[Assistant] I do not expect to be acknowledged, but if I am, I'll be looking for spelling.


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[Assistant] The Parker square is thanks to Bradley Herron. Consider this a sign of my appreciation. Mate, mate indeed.


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[Assistant] So people, I'm going to say this now because Matt has helped Numberphile so much over the years. I owe him so many favors because he's been in so many videos for me. If you buy a hardback edition, a Bradley edition while they're available and you ever cross paths with me, I will sign it as Bradley.


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[Assistant] Which is something I normally refuse to do that on the previous. So if you ever come to me with a humble pie, hardback edition by Matt Parker, I'll sign Bradley Aaron on the page.


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[Assistant] I also want to know if for your author picture in that paperback edition, you're going to...


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[Assistant] There are many things I wanted to talk to you about, and we haven't got time.


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[Assistant] Like, so you will come back and do another podcast soon?


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[Assistant] But there's one thing we have to talk about in this episode and we've already mentioned it, but I know people are going to want to hear you talk about it. And that is the Parker square. So for people who don't watch number five videos, how would you give an executive summary of the Parker square story and how it rose to fame? So the Parker square. You don't have to go into all the math. I'll link to the video.


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[Assistant] Somewhere on that spectrum, it's kind of starting to morph into a mascot for failure and getting things wrong rather than noble effort.


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[Assistant] How much does it like, cause obviously my exposure to your life is limited to numberphile. So to me, the Parker square and Matt Parker have become very, very closely entwined and I can't upload a video with you without Parker square jokes and how much does it follow you around? Like, you know.


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[Assistant] If you could go back in time, you can't, but if you could go back in time, would you not do that video? Would you think, oh, it's just been ever. I would happily put it out.


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[Assistant] Parker square of Parker squares. So minus spoiler, but if you do have the hard copy, which I hope you've all gone out and bought by now, you just have to flick to the back of the book to page.


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[Assistant] Nine? Page nine, yeah. Page nine. Which is also a bit of a spoiler to the numbering system in this book.


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[Assistant] And there is, there indeed, there is a big montage of pictures of Matt with people wearing Parker square t-shirts, which, uh, which, yeah, I must have a little chat to a penguin about royalties on that. Brilliant. Thanks so much for your time again.


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[Assistant] People, if you'd like to get your hands and eyes on a copy of Matt's book, the best way is via his website, Maths Gear, and I'll include a link in the notes for the show. That'll get you a copy signed by Matt, and it also means you'll get your hands on it, perhaps before the book is even officially released in your particular part of the world.


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[Assistant] More details in the notes, go and have a look. My thanks also to the Mathematical Sciences Research Institute for all its support of Numberphile, and a double helping of thanks to Maya Sound.


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[Assistant] Berkeley based audio company, which kindly made this particular episode possible.


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[Assistant] Again, links to them in the show notes. If you'd like to find out more about Numberphile, maybe even support us yourself, check out the links and all sorts of good stuff at numberphile.com. I'm Brady Haran and I'll be back again soon with another episode of the Numberphile Podcast.


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[Assistant] The reason for that is, it will happen. There will be another pandemic.


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[Assistant] So having seen him do it a few times, I begged him to tell me what was going on because I was starting to get interested in card tricks myself. This would have been the late 90s, I guess.


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[Assistant] And there were times that a couple of rather important national talks in the US where he forgot to show up in his later years and that, that was embarrassing because, you know.


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[Assistant] And in fact, one of the talks he gave, he gave a few talks, one was on can you hear the shape of a drum, which he gave to an applied mathematics class, which was supposed to last for 50 minutes. And he went on for I think a little over two hours.


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[Assistant] But was marked by this free-spirited, fun-loving and playful approach to everything, which, which distinguished him from, you know, some other big shots who also did very serious mathematics. He had a flair and a passion.


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[Assistant] You know, game of life, which people are still playing and many other things.


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[Assistant] I think, you know, his, his, his originality, his original approach and spirit, I mean, there's very few people in the last 50 years, I can only think of one or two who, who developed


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[Assistant] Today's guest is Ben Sparks. Ben's a teacher, a public speaker, a math popularizer. In fact, as you'll find out today, he's a man who wears many hats. And not all of them are great fashion choices.


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[Assistant] Hopefully, you might already know Ben from his Numberphile videos, which are always favorites with our viewers. They include amazing explanations of the Mandelbrot set, and an explanation of why the golden ratio is so irrational. But this interview starts with a topic I always find personally fascinating.


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[Assistant] It's been really often I ask people about like, their childhood and their really early days. I'm really excited to ask you about this, because if memory serves correctly, you are a twin.


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[Assistant] Alright, we'll link to whatever we need to so people can go and check him out.


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[Assistant] I'm sure you've just told me in conversation. I'm sure you've told me multiple times it's come up. Just, you know.


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[Assistant] So what's an example of that? What's like, if you haven't seen him for a while, what's something you catch up, what's something that will make you guys go, oh, whoops.


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[Assistant] I mean, a lot of people get that from their parents, don't they? Like, oh my goodness, I'm turning into my mum or dad, but you've got someone who's your exact same age.


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[Assistant] I'm not going to be able to continue podcasting until I see a picture, so hang on. Let me have a look. Where do I find him? What's his website or something or?


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[Assistant] Oh, Ben, you freaked me out. I've got another friend who's an identical twin, and the first time I saw his twin, I was like, it really weirded me out.


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[Assistant] Let's talk about you, but I may have occasionally asked you a Tim question, saying you've got this parallel, parallel life going on. Were you good at mathematics when you were little?


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[Assistant] Yeah. But would you have been like top of the class? Would it have been, you know, Ben always gets the highest mark on the math test?


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[Assistant] So as you, as you, in those sort of, you know, early years of school, primary school through high school, what did you want to be? What was your, like, you know, if someone said, oh, hello little Ben, what do you want to be when you grow up? What would, what would that Ben likely have told me?


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[Assistant] As a musician, what we, what band, I know you play guitar now, is that what you were playing then or what, what did you play?


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[Assistant] What was your, what was like the go-to song for you guys? Did you have like a party trick song? Like, like everyone has a karaoke song? What would, what would, what would Tim and Happy Tim sing if they were like, if everyone was like, come on, sing us a song guys.


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[Assistant] At what point then in high school did it become apparent you were going down this mathematics track?


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[Assistant] How did you find the hole from being probably, I imagine, you know, a big fish in a small pond to being, you know, just a guy doing maths at Oxford with all the best people in the country there?


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[Assistant] It just sounds like you had a good work-life balance to me.


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[Assistant] Ah, that's amazing. So as you progressed through your years at Oxford, tell me about how your relationship with mathematics was changing.


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[Assistant] Had that been the plan, Ben? Like as you were coming towards the end of university, there was never thought to, you know, I'm going to become a math professor or I'm going to go and work in the city and make a, you know, work in the share markets and stuff was, was.


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[Assistant] Teacher always the next step or did you kind of just fall into that? Like in that last year of university, you must have been thinking, oh my God, what do I do next?


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[Assistant] Sorry, can you tell me again, what were you teaching there? You were teaching math?


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[Assistant] For our listeners, I mean most of our listeners probably aren't British, can you explain what that means?


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[Assistant] This is converting graduates who maybe didn't want to be a teacher into a teacher in a sort of a one year condensed course.


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[Assistant] So you, so you do this conversion. You've converted into a teacher in this one year course. Where do you go from there?


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[Assistant] That's really interesting, Ben, because so many people I've spoken to have told me this kind of story that


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[Assistant] At school, they felt like mathematics was just solving problems and like, you know, brute force. Yeah. And then it was when they got to university, this magic door opened and they realized it was not what, it was something else. It was something more amazing.


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[Assistant] But it sounds like your university experience was almost just more problem solving and worksheets and tests and things. And it wasn't until after university you got this, this new insight that turned, that switched you.


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[Assistant] Almost invariably we stumble across, you know, an inspirational teacher or someone along the way. Did your inspirational teacher come when you were learning to be a teacher?


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[Assistant] I feel like just for the sort of the sake of the thread of the podcast, we should quickly touch base with your grumpy twin and find out what he's up to at the moment.


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[Assistant] He'd gone to Cardiff and studied what? Something musical or?


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[Assistant] Short straw didn't take off though. They've, uh, they've retired now.


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[Assistant] And just quickly, has Tim become an engineer? Does he work as an engineer now?


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[Assistant] All right. Jack of all trades. Let's go back to you though. You've, you've, you've finished this conversion, this teacher conversion course. Yep. That's one year. Yep.


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[Assistant] I had a very good school experience myself, but I still have like anxiety dreams that I'm back at my school that I was at as a kid. Like it's an uncomfortable dream and you've actually gone back there to work.


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[Assistant] I like that you almost sounded a little bit boastful that you got to go in the staff room.


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[Assistant] There's every time you have to go into the staff room, like, I'd like you have permission. Can you please pass this note to Mr. Jones? He's in the staff room and you get to go in. It is, it's like, it's like the Holy Holies, isn't it? You're like, I can't believe I'm getting to see this. This is amazing.


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[Assistant] But now you're in the staff room for real, like you have like the whole access pass.


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[Assistant] So because you've done those few years teaching, you're actually starting to look at your lecturers through a different prism now.


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[Assistant] It must help you when you're making a Numberphile video with me and you see that confused look on my face. Oh, does it ever leak?


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[Assistant] And what you would busk, just go and earn money by playing in the streets, would you?


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[Assistant] Should have had the hat, the hat could have made the difference. Where did you go in the travels? Like, you know, you don't have to give me the full itinerary, but what kind of parts of the world did you find yourself yet?


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[Assistant] Oh, Rundle Mall's a great place for busking. You would've covered your cost if you'd gone there.


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[Assistant] Alright, yeah, you do, you do have to go there. So during these busking, you know, your traveling busking period. Yeah. Does mathematics play any role in your life whatsoever at this point? Or is this, it's, it's just, it's just parked for now. Now you're just like seeing the world and it's about the music.


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[Assistant] I guess when you're busking in the street asking for coins, you really need to do something to get your cred up a bit.


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[Assistant] All right. So you've, you've devoted some time to your travels and music. You've got to end this Bohemian lifestyle at some point. What happens? What happens? Really? Do I have to? Well, I don't know. Maybe you don't. What happens next?


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[Assistant] Did you take m-marking exams then as like, is it a really s- big responsibility to you, or do you become blasé about it? Like, I'm fascinated to see behind that curtain.


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[Assistant] That's great talk. I was relaxed. Great Numberphile video people. Make sure you check it out.


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[Assistant] Were they more just trying to justify that huge beard and bushy hairdo?


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[Assistant] So this was just being invited to come and give like, you know, one-off special presentations, not to come and be their new maths teacher.


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[Assistant] They clearly wanted to offer you the job but knew you didn't want it. So he like, he played you like a cheap guitar.


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[Assistant] What's this, what's this group? Ben, this is an organization that provides what?


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[Assistant] So you'd go, maybe you'd go and sometimes you'd go and inspire teachers. Sometimes you'd go in front of a group of a few hundred students and just like, you know, wow them for half an hour and make them think, oh, maths is cool.


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[Assistant] So while you're at the college for five years, you're doing a bit of work for this organisation on the side, like they're basically engaging you as a freelancer to go and do talks.


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[Assistant] So half your time's, what's it called, ASMP?


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[Assistant] So half your time is AMSP and half your time is whatever you choose. And that can be all sorts of different things.


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[Assistant] So tell me about that other half for a second. I know occasionally you do number five videos, obviously. That's the part I know about. What else do you do with this huge wedge of time that is yours to be creative with and earn money with?


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[Assistant] Your adventure so far sounds very- it sounds like very piecemeal and very-


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[Assistant] Like, it's not very typical. Have you been satisfied? Are you satisfied with it? Like, has it made you happy? Has it been what you expected? Has it been? Like, how do you feel about it when you, when you tell the story of it now like this?


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[Assistant] I guess your main, your main job now then when you really boil it down is getting up in front of a group of people and talking to them about mathematics.


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[Assistant] I know there's a million ways to answer this question and you, and you could do a whole course on the answer to this question. So please don't. But, but what do you think the secret is to successfully talking maths in public? Like if you were going to just cherry pick one or two little.


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[Assistant] Nuggets for people who might be listening who are math teachers or are just curious about what makes people good at it. Can you think of like a little piece of advice or something that you think works that not everyone necessarily thinks of?


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[Assistant] Why is that fuel? Just because if something fascinates you, you just naturally want to know more about how it was built sort of thing.


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[Assistant] There are only certain people that will be motivated by that though, won't there? Like if you- Oh, oh, that's true. Yeah. Like if you show someone, if you show someone the Mandelbrot set, I think there's a certain subset of people that will go, that's beautiful and fascinating. I want to know more. But I can think of a lot of people in my life who would look at that and just like, it would just, they'd go, what, what a mess.


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[Assistant] I've seen you give a few talks and obviously I filmed you making a number of our videos and I can see, you know, the tricks you use and the inspiration you use and you obviously use humor a lot very cleverly as well. So, and like, you're obviously very good at that. The thing I want to ask you though.


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[Assistant] Is about talking to a group of mathematics teachers. Cause I do talks as well and I quite enjoy doing talks. There's nothing I find harder than talking to a room full of mathematics teachers. Like that is, that is a completely different beast.


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[Assistant] But they're also there, their motivation is very different to other audiences I find. They don't, they're like, you can keep your math tricks till the cows come home, that's not going to help me in my job. And the reason I'm here is because I need help in my job.


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[Assistant] What do you want to be doing next then? You seem to have this big tumbling from one thing to the next. Like is there, have you got like this end game or grand thing or is what you're doing now good for now?


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[Assistant] Oh, I dunno. I think you could always do more numberphile videos. I'm totally in favour of that.


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[Assistant] And finally, you mentioned we're in lockdown. Are you having a lot of contact with Tim at the moment?


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[Assistant] Oh no, I know the Numberphile audience. If I don't find out what games you're playing, they'll be like a riot.


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[Assistant] Well, in the notes for this show, people, I will be linking to most importantly, Ben's website and you can get in touch with him. Uh, you can see all sorts of things he's up to. Very importantly, you can book him in for a talk or something when all this lockdown shenanigans ends and get him to come out because Ben's talks are excellent. I've seen a couple in there.


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[Assistant] They're definitely worth, worth your time. Thanks Brady. And I also will link to some of Tim's music so you can check out what he's up to as well.


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[Assistant] Well I did have an idea actually, because I do use little bits of interlude music just to break the interview up and at the start and the end and I do have like number 5 music. You could do your rendition of the number 5 music and I'll use that as all the little stings and ends and things like that. Could be you playing. And I'll tell people that at the end as a surprise.


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[Assistant] So, as, uh, Ben plays us out on the guitar, my thanks to him, and to his twin, Tim, who was unwittingly dragged into this episode. There are links to everything we discussed today, and Ben's website, of course, in the video description. I'll also link to Ben's Numberphile videos.


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[Assistant] In Berkeley, California. It's also made possible by support from people like you, listeners and viewers via small contributions on Patreon. If you'd like to help us out, it really makes a difference. Even like a dollar a month goes a long way. Go to patreon.com slash numberphile.


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[Assistant] Thanks to those of you who already support us. Your names are all listed on our wall of fame. I'll link to that as well in the description.


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[Assistant] I'm Brady Harren, we'll be back again very soon, with another podcast.


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[Assistant] Today we're talking with set theorist Asaf Karagila. He's based in the English city of Norwich, working at the University of East Anglia. There his research involves exploring the mind-bending world of infinities.


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[Assistant] But before we get to these lofty concepts, let's start in the desert and an unconventional route to academia.


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[Assistant] When you grow up in the desert, is it like, how's your childhood different from people who don't grow up in the desert? Like do you have, do you play different games and do different things as a boy? No, it's just hotter and you get used to it.


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[Assistant] What were you into as a boy? Like when you were a young boy, what were your obsessions? Were you obsessed with sport or were you already obsessed with mathematics or?


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[Assistant] What did you want to be when you grew up? Like if I'd said to the little boy, hey, what are you gonna, what job would you want to do when you're an adult?


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[Assistant] Okay, not too rebellious, they're just mild rebellion. Yeah, let's not go there.


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[Assistant] So just to make sure I understand the path properly. You joined the military, presumably that was compulsory, it's a compulsory service in Israel. You joined the military, you got a taste for computers and computer science and thought you liked it. No, no, I already like computers.


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[Assistant] Okay, so you already, you already, and after doing it in the military, you thought you wanted that as a career. You went to, you couldn't get into that particular course at university because you had the insufficient schooling. They said use the mathematics as a shortcut to get into computer science, but then mathematics grabbed you.


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[Assistant] Right, because you were already a bit of a computer nerd, so they were like, let him do his thing. He's best left alone. So during this like, first semester of mathematics, when it sounds like mathematics kind of re-ambushed you a little bit and drew you back in, was it inspirational teachers? Was it the content? Do you remember anything specific that really, just really hooked you in?


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[Assistant] You talked when you were young about liking sort of dinosaurs and fighter jets and those typical things that we all like when we're young. Another thing I know that does really inspire the young mind is the notion of infinity. When you, when you're first young and you find out this thing called infinity exists.


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[Assistant] Do you remember infinity from when you were young? Like, oh, what's bigger than infinity? Can I count to infinity? Or was it something you didn't really encounter until later?


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[Assistant] But leaving high school can knock you off the path, can't it? To get into the cool stuff later, like university. It turned out well for you, but even you encountered that problem when you tried to get into the computer science at university and they said, no, the door is shut to you because of being a high school dropout.


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[Assistant] So tell me more about this, you know, the falling in love with set theory and falling in love with mathematics at university. It sounds like it was like almost a sort of a love at first sight on this reintroduction.


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[Assistant] I talk to other mathematicians sometimes about their path through university and the different, the different branches of mathematics they experienced and how they eventually gravitated to one over another. It sounds like you were all in on set theory really early.


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[Assistant] So set theory at its core is about dealing with infinity and infinities.


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[Assistant] Yep, so that's like your, that's your ultimate set, all the numbers, that's like your, that's your dream set.


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[Assistant] What advantage do sets have that I don't have if I'm just dealing with individual numbers on their own, like number theorists and things like that? What's the power of a set?


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[Assistant] At what point does a set give us the power to unlock all these mysteries of infinity? Or what is it about the set that gives us that power?


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[Assistant] Let's go back to university. At university did you have this same rebellious streak that you had in high school? Were you cutting courses and things like that or were you suddenly finding yourself more diligent now as a student?


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[Assistant] As you come towards the end of your undergraduate course, are you thinking, this is it? This is my career? Or what are you thinking your career progression is going to be from here?


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[Assistant] I won't ask for technical details because A, I won't understand and B, this is a podcast, so it makes it even harder. But who found the mistake, the stone at the bottom that had the floor? Was it, was it you? Was it, uh, like a third party reviewer? How, do you remember how the mistake was found and what that felt like?


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[Assistant] Now as a, you know, professional mathematician moving, moving up the rungs, did you take lessons from that? Has it, has it made you more thorough or cautious or careful of those foundation stones or, you know, did it teach you a lesson?


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[Assistant] The stuff you publish is the stuff you get right.


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[Assistant] Hopefully, most of the time. So all those, all those wrong moments, all those false starts and dead ends that you've experienced, you know, don't get published. So the wider mathematical community doesn't know about them. Who does know about them?


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[Assistant] So when mathematicians get together over a beer or a coffee or a chat and they just tell war stories as you put it, are often those stories about things I once got wrong, you know, classic mistakes I made.


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[Assistant] Yeah. Okay. So, after you've done your PhD, what's the next step in your career from there? What do you do next?


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[Assistant] So for people who don't understand, this is a fellowship, it's a sort of a pot of money they give you to fund, fund your life and your career while you're doing postdoctoral studies, while you wait for that next big career step.


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[Assistant] So the Newton Fellowship that you had been given to spend two years as a postdoc, what university was that going to be at?


[User] Please transcribe this text

[Assistant] So it was a good place to go for a postdoc. So for two years, you're doing a postdoc here at UEA with this Newton Fellowship.


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[Assistant] What do you do? Because you're kind of, you're not the boss. You've got a, you've kind of got a boss, but you're also not like the bottom of the heap anymore. You're not like, you're not, oh, you're not like a PhD. When you're doing a postdoc in mathematics, what are you doing? What work are you doing and who for? And to what end? There are two types of postdocs.


[User] Please transcribe this text

[Assistant] So that, so they've got a big project and they might have you helping like with grunt work or side projects. Okay, yeaah.


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[Assistant] What, what are the stakes? What, what's on offer here? What are you, what are you asking UKRI to give you?


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[Assistant] But the thing is, from everything you tell me, from even when you were in high school, it sounds like you're someone who doesn't like to be told what to do and you want to do it your way. I can imagine you walking in in jeans and a t-shirt and saying, take me or leave me, this is what I am. But you, you conformed on this one.


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[Assistant] From what I know of the little bit I know of you today even, you really are enthusiastic about outreach and communicating your subject and things like that. Are you saddened to not be teaching? Would you like to be teaching students?


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[Assistant] What do you want to achieve in the next maybe seven years? Is there some huge problem in set theory? Is there a million dollar proof that you want to find? Or is there like, what's your holy grail now? What are you working on?


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[Assistant] So this partition principle, is it, that's your kind of like your white whale or Moby Dick, is it? It's like your thing you'd love to crack.


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[Assistant] Is it a really famous problem? Like would everyone in set theory know about it or is it more just your, your problem or is it like, is it the big, the big trophy that everyone in set theory talks about?


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[Assistant] Alright, well I'll come back in five to seven years and you can tell me how you did it.


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[Assistant] Alright, two years. You described to me earlier that set theory is right at the frontier, like at the extremities of where you can go, which you put it in a really nice poetic way. Are you just being really biased or would most people say set theory is right at the limits of


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[Assistant] That's all for today, but please see the notes for today's episode for more links and information.


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[Assistant] Thanks to the Mathematical Sciences Research Institute in Berkeley, California for its support of Numberfire. And also thanks to the UK Research and Innovation Future Leaders Fellowship for their help with this episode.


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[Assistant] So, like Martin just mentioned, I'm a, uh, classically trained university, uh, trained composer. I'm from Perth in Western Australia, which is where I...


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[Assistant] I did all of my undergraduate studies and I have kind of, yeaah, I was playing bass in a lot of different bands, kind of taking life pretty easily, not too seriously, and I did that for about 10 years touring across Australia and


[User] Please transcribe this text

[Assistant] Uh, Europe and Canada. And then I decided it was probably time to take life a little more seriously. So I went and did a teaching degree. So for 10 years I was teaching high school music, uhm, in Australia and also in the UK, uh, for about 4 years, which I, I really loved.


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[Assistant] I've been in Vancouver for four years, uhm, I married a lovely Canadian lass, and uh, here I am. I've kind of revisited my composition roots, so I've been pursuing composition for film and television.


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[Assistant] Uhm, I've just wrapped up doing the music and actually the whole audio post production on this film. Yeaah, so that's kind of where my energies are focused these days in composition. And when Martin came to me, in December last year,


[User] Please transcribe this text

[Assistant] With this project, uh, it didn't take a lot of convincing. I can see his, like, passion and his energy, his excitement and enthusiasm for art and, uh, science. And yeah, those, those passions really match my own. So this was a very easy project to say yes to.


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[Assistant] Yeah, yeah, that's what I tried to communicate to my students. Uhm, it really is, uhm, math made audible.


[User] Please transcribe this text

[Assistant] And uh, yeaah, like telling that to students in the classroom, you could see.


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[Assistant] Let's see if you light bulbs kind of switch on and, uh,


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[Assistant] Yeah, and I tried to make the connection also with visual art as well. There's a lot of strong kind of parallels between the music that I've composed for this, uh, for this project. Because a lot of the music is inspired by 20th century piano music. Yeah, I always used to draw those parallels between what was happening musically and visually in the 20th century.


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[Assistant] Definitely that was a big concern of mine, uh, making the music, uh, playable and accessible. And I kind of, as the project kind of progressed, I kind of realized there's a pedagogical aspect to this, this project in that it's kind of, um, introducing a lot of, all of the pieces are kind of based on, they have like models, uh, from


[User] Please transcribe this text

[Assistant] You know, uh, composers in the 20th century. So I realized there's this kind of, it's like a gateway, an introduction into this challenging listening.


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[Assistant] So this piece is heavily based on like the minimalist work of like, uh, Steve Reich, Philip Glass. Uhm, so this, this polyrhythmic nature of the, the mathematical material fits so well into that, that musical language of minimalist piano music.


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[Assistant] As the piece progresses, we've kind of, uhm, I've used a technique called serialism, which encodes various musical elements such as articulation, dynamics, uhm, pitch.


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[Assistant] It ascribes them a number, uh, which we've matched the digit, obviously. And then, um, yeaah, as the piece goes, goes along, we've counted the, the occurrence of the notes, and then used that frequency of occurrence to, uh, inform the, the serial kind of nature of the piece.


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[Assistant] Yeah, yeah, it, it starts at that point and then it really kind of...


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[Assistant] It blows out very quickly, uhm, and that's quite apparent as you listen to the piece.


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[Assistant] The model for this piece is, uh, the multiple serial works of Stockhausen and Boulez from the mid 20th century. And this is like hardcore intellectual academic music. It's not written to be easily listened to or easily digested. It's really impenetrable. And I've kind of towed the balance between


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[Assistant] Making those ideas, uhm, apparent, but also making something that's a little more accessible and listenable for, you know, the modern audience, I guess.


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[Assistant] Uh, unfortunately, my piano skills aren't up to performing these pieces. Uhm, and we just kind of ran out of time to organize a performance. That would have been really fantastic, and we may still do that in the future. But in the interest of time, we just had to...


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[Assistant] This was pretty intense, to be honest, uhm, cause I'm just...


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[Assistant] Literally just working with a stream of pitches, which doesn't make any traditional kind of musical sense. So the feeling of it for me was kind of like a jazz pianist just playing almost like a free jazz kind of solo.


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[Assistant] Uhm, which are kind of like sharp, jagged, accented chords that kind of...


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[Assistant] Outline the harmonic structure. That was kind of the basis for my input into the piece. The piece modulates, so it changes key every 10 bars. And because we've got 120 bars, there's 10 modulations through 10 different keys, which are all derived from a scale called the decatonic scale, which I was unfamiliar with until Martin shared a wiki page with me.


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[Assistant] I guess, like, because of my background and understanding of, uh, you know, listening to challenging music, I wasn't too, uh, phased by having, you know, non-musical kind of pitches and information being thrown at me. Uhm, it was more a matter of just kind of, you know, working within those constraints, I guess.


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[Assistant] Yeah, yeah, uhm, that's a really good point and something that we kind of, it was kind of different for each piece and this piece was one of the more constrained pieces for me. Uhm, I had to accept what was in the right hand, the numbers were what they were.


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[Assistant] Uhm, I couldn't change that. For me, I just had to create a harmonic structure and a harmonic movement in the left hand that kind of supported and, uh,


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[Assistant] Yeah, for sure. That was kind of Martin's kind of purview. He kind of came up with all the...


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[Assistant] I guess this was one piece where I kind of took a little bit of liberties with the data. Martin was kind of keen for me to kind of stick to the


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[Assistant] The, the literal interpretation of the data as much as possible, but this is one where I was like, okay, if we, if we're kind of aiming at this RTS kind of sound, then we need to have repeating phrases. We can't just kind of be following like a random string of numbers. So I kind of, uh, pulled a little bit of weight in, in that one.


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[Assistant] Yeah, one of the points that I made to Martin early on in the process, uhm, was that the more highly organized music is, historically speaking, uhm, the less like music it sounds. So I was, you know, as the composer involved in this project, I was very aware of kind of maintaining that balance of


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[Assistant] You know, respecting the data and the numbers, but trying to inject, you know, some musicality and humanness into the equation as well.


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[Assistant] This was actually a reverse engineered piece as well, so I'm a huge fan of Morton Feldman's piano work. He was an American composer in the 1950s, 60s, working at the same time as composers in Europe, like Boulez and Schochhausen, but with a very different approach. The Europeans were much more, uhm,


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[Assistant] There's nothing louder than a mezzo piano. Just dynamically alone, that creates a mood and creates a feeling. And in terms of the encoding of the digits, uhm, I think I will leave that up to Martin.


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[Assistant] Uh, so we've taken, uhm, all of the digits up to the finite point and every nine, uh, we've taken that as an event and then we've summed the, summed the digits between each nine, uhm, and I've used that number as, uh, the time signature.


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[Assistant] And the track ends at the final point. It also marks there's, uh, I think there's five or six double nines between...


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[Assistant] The start and the Feynman point, and so we've marked those with kind of musical ideas as well. Yeah, and so there's various kind of, uh, the music itself has a kind of jocular rhythmic nature to kind of reflect the nature of the joke that Feynman is making here. Hopefully that comes across.


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[Assistant] For me it's the null, because I think the null...


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[Assistant] Is the truest representation of what pi is. The piece null just kind of exists in and of itself. It doesn't ask anything of you, doesn't expect anything of you, it just is. Uhm, and for me that's a good representation of the number.


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[Assistant] Uhm, actually, I was thinking about this morning, and I was thinking, because we did have a limited time frame, we had about five weeks to kind of get this together, uhm, I would really like, uh, an extended period of time to kind of really sit down, knock out some ideas, uhm, compose them, get them performed.


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[Assistant] Today's guest is Vicki Neal, a mathematician at the University of Oxford. She's just written a book about why people should study mathematics at university. So of course, I wanted to find out why Vicki studied mathematics at university.


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[Assistant] So the beginning is always a good place to start. Where are you from? Where were you born?


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[Assistant] So when you go to Wooster or Wooster comes up in conversation, do you feel any warmth or attachment to it because you were born there or is it just like complete coldness?


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[Assistant] Tell me then what you were like as a youngster. Would I have seen like little girl Vicky and said, well, she's going to be a mathematician.


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[Assistant] What did you want to do when you grew up then? What would the answer have been when the adults said and what do you want to be when you grow up Vicky?


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[Assistant] What about sort of family and friends, parents and things like that? Were you surrounded by mathematics and mathematical people or like what did your parents do for example?


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[Assistant] When you look back at your maths education at school, like the people I speak to, I get such mixed responses of how I look back at some people it was just this wonderful warm experience at school, other people it was like this dreadful


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[Assistant] Terribly taught thing that they kind of persevered with despite how would you describe your school mathematical education?


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[Assistant] Were you then taking those concepts back to the classroom and bamboozling your teachers or?


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[Assistant] Besides music and mathematics, what might I have found you doing? Would it be kind of the nerdy stuff like Rubik's cubes and puzzles and games? Or would I have found you playing hockey or watching TV? What else were you into?


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[Assistant] So as high school started drawing to a close and you had to like start making actual decisions about university, what was the thinking and what were the decisions that were made?


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[Assistant] At that point, at kind of sixth form, this is, you know, the very end of high school.


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[Assistant] You're choosing to do mathematics at university. Is this because you've just got this insatiable love of mathematics or at this point are you starting to see a career path?


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[Assistant] Did you compete in any of those Math Olympiads as a school student?


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[Assistant] What was it like going to Cambridge then, going from, you know, school level mathematics to big league?


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[Assistant] Was the demand difficult though? I hear from a lot of people that go to Cambridge that suddenly think, God, I've got to work so hard. And this is like, it's like a real change of gears. Did you not find?


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[Assistant] And also obviously you've probably gone from being mathematically a pretty big fish to just being another


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[Assistant] Person who's pretty good at mathematics, like suddenly you're surrounded by the cream of the crop. How did you find that adjustment?


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[Assistant] I don't think I've ever spoken to someone who sounds like they were so prepared for university and found the transition so natural.


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[Assistant] And then how was your undergraduate sort of years at Cambridge? How did things evolve for you there?


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[Assistant] At what point did it become clear that, you know, you were going to go further than just an undergraduate? Like you weren't going to go off to the city and become a stockbroker.


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[Assistant] How does life change when you go from undergrad to masters to a PhD? Like how does life change and how does the mathematics change?


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[Assistant] And obviously other ones did. Can you tell me about the bits you liked and didn't like and why you think that's the case? Like is it just the wiring of your individual brain? Was it just the personalities of the teachers you had? How does that unfold?


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[Assistant] A lot of mathematicians when I've spoken to them about this stage in their career,


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[Assistant] I've been surprised by the number of them who've talked about how they made a choice based on groups of students they liked or a supervisor they liked and things like that rather than the mathematics itself. It sounds like your decision making though was based very much on the work, the content.


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[Assistant] Do you look back at your PhD thesis fondly? Did you discover something interesting?


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[Assistant] Also, Hardy, Littlewood, Green and Tao, you're dropping, I'm no mathematician and even I know their big names. Yeah, they quite get names to drop, don't they? Yeah.


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[Assistant] So at any point during the PhD, did you have that feeling that, oh, I'm not going to do it? It's going nowhere? Or were you, did you steer the course pretty well on that spectrum between despair and cruising easily? Where, where did you fall?


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[Assistant] So you've got your PhD, congratulations. Thank you. Now what?


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[Assistant] Alright, alright, I'm gonna try to say that. Supernumerary fellow? Very good.


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[Assistant] I want to talk to you more about sort of outreach and books and a few other things you've done because that's obviously what you're known for and you're a bit of a superstar in that area. But before I flatter you by talking about that, let me ask you this.


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[Assistant] The math pecking order amongst all the big wigs in the coffee room, you know, the people who, who are doing like, you know, pure research and things like that. Do they respect and love the teachers or is there kind of like this, this sniffiness or I always wonder about that.


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[Assistant] Who inspired you when you were younger? Do you ever wish that that was your job? Like, you know, solving the Riemann hypothesis?


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[Assistant] I want to ask about your latest book, because I'm very curious about some of the things in it. But before I do, I want to ask you about mathematical craft.


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[Assistant] Tell me about mathematical craft. What does that mean?


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[Assistant] I'm looking at a picture of it now. It sort of looks like, you know, like you say, like a torus, like a donut made of all these tiny little beads. And the one I'm looking at here, like most of the beads are blue, and there's this just random scattering of gold beads amongst the blue beads, and presumably those gold beads represent the distribution of the primes.


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[Assistant] That's the one. Before we talk about the question of why study mathematics, let me ask you, why is there a polar bear on the cover?


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[Assistant] You have to buy the book if you want to find out why there's this huge polar bear's head peering out of the cover at the potential readers. It's a great polar bear.


[User] Please transcribe this text

[Assistant] What is the point of this book? Why study mathematics? What's the book trying to achieve?


[User] Please transcribe this text

[Assistant] So it's quite like a focused book. It's not just for the person in the street who, it's not like one of these popularization math books that someone like me would pick up just to.


[User] Please transcribe this text

[Assistant] Is this kind of a bit like a lonely planet though? Like are you saying, well, if you go to the University of Nottingham, you'll get this. And if you go to Cambridge, you'll get this. Like are you, are you making that granular a comparison or is it more sort of broad brush overview and you're not sort of naming names?


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[Assistant] And you also mentioned, uh, briefly the pandemic that everyone in the world is living through. Is your book pandemic-proof? You know, if you're writing about what it's like to go to university and be taught, and it seems that how we're being taught at university


[User] Please transcribe this text

[Assistant] Is changing at the moment. Like, how's that an issue for you?


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[Assistant] Did any part of you feel like, you know, you were at a sort of a friendly competition or as an advocate for mathematics against those other subjects, like you're having to make the case, come and study mathematics instead of history? Is that part of this?


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[Assistant] It sounds like, you know, you've had an education and a career that's had its usual share of ups and downs and challenges and things like that. But generally it sounds like it's been fairly smooth sailing and it's also been a bit of a fail complete that you would be a mathematician.


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[Assistant] Does that make you the best possible person or the worst possible person to be counseling us about why study mathematics?


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[Assistant] Why someone should study mathematics. If someone's out there and they're at that crossroads and maybe mathematics is for them, maybe it's not, and they're having to make that key decision.


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[Assistant] And I know everyone's different and has unique circumstances, but could you perhaps give us one reason why they should study mathematics?


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[Assistant] You can find out more about Vicki, her work and of course her books by checking out the links in the notes from today's episode. Numberphile is supported by the Mathematical Sciences Research Institute. Again, there's a link in the notes. I'm Brady Harron and you've been listening to the Numberphile podcast.


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[Assistant] Today our guest is the astrophysicist Katie Mack. Now when she's not pondering and coding the secrets of space, Dr. Mack's well known to many as a popular scientific tweeter at Astro Katie. And she's also the author of a new book about the fate of the universe. We'll get to all that later.


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[Assistant] And, this being Numberphile, you can also rest assured I'm pretty curious about the role of mathematics in the life of a cosmologist.


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[Assistant] Because you're Katie on your book, but you're Catherine on your papers.


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[Assistant] There's no possibility of switching to Katie on your papers then because then it will cause this kind of disjoin or-


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[Assistant] If I had been following your childhood, at what point would I have said, do you know what? I think that girl's going to become an astrophysicist.


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[Assistant] So, athletics and sport was like a proper option, was it?


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[Assistant] Alright then, so through high school and whatnot, then a school, you were like pretty academically sound then, were you like, you know, the top of the class, physics, mathsy person?


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[Assistant] What was your attitude to mathematics at this point? I have to ask because it's the number four podcast. Obviously you've got these physics aspirations, but mathematics is so intertwined with physics.


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[Assistant] I get the impression from that little bit I've read about you that you had quite a good family for where you wanted to go. Like you would have probably had parents who were quite encouraging.


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[Assistant] I read that your mother encouraged you to watch Star Trek and Star Wars.


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[Assistant] Can you tell me a bit more about the mathematics thing then? It sounds like you said you kind of felt like you were a bit behind the curve to start with because of the alternative education. Yeah, yeah. Like was that dangerous? Did you feel like you were sort of sinking at any point or was it something you always had well in hand?


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[Assistant] You said that you did physics because you wanted to keep your options open.


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[Assistant] Were you ever tempted or nearly seduced away from that cosmology astrophysicist path? Like were there other things you saw that you thought this might be for me or did you pretty much stay on the straight and narrow throughout?


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[Assistant] That looks really cool inside. It looks like an art installation. Did you get to go in it many times?


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[Assistant] Very cool. Alright, so you started with the particle physics. Yeah. What happened next? How did you, what was the path? Give me the executive summary.


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[Assistant] Help me understand being a theoretical cosmologist or theoretical astrophysicist because what does your work look like? Take away the teaching, take away outreach and all the kind of.


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[Assistant] Dream up some idea and then do a few sums and think, oh, yeah, that could work. And then then what? Like.


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[Assistant] What happens if you are lying in bed one night and you come up with like, you know, the theory of how the universe is working and it's something that can't yet be or hasn't been measured and can't be measured or observed.


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[Assistant] What do you do when that happens what do you do when your idea is something that hasn't can't be looked at with a telescope yet.


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[Assistant] Take this quick tea break to remind you that this episode has been sponsored by G Research, a world leading quantitative finance research firm based in Europe. And if you find quantitative easy to say, well, you're a better podcaster than me.


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[Assistant] Now G-Research is hiring clever people from around the world to tackle the biggest questions in finance, applying the latest in machine learning, big data, all the top technology.


[User] Please transcribe this text

[Assistant] G-Research is always looking to hire the top STEM talent, so if you are good with numbers, mathematics, computers, that kind of stuff, well maybe this could be the opportunity you've been waiting for.


[User] Please transcribe this text

[Assistant] I know G Research takes real pride in the culture they've created and they're keen to nurture future talent. To find out more about them, go to gresearch.co.uk slash numberphile.


[User] Please transcribe this text

[Assistant] G-Research. Create today, predict tomorrow.


[User] Please transcribe this text

[Assistant] Can I ask you about Twitter? Sure. One of the things you're quite well known for, how I first knew of you, is for being Twitter famous. You're kind of the first scientist to become really mega followed on Twitter and you're the person to follow and you're still one of the most followed scientists out there.


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[Assistant] Then what happened though? I thought you made a couple of clever comments and a couple of smart remarks and things kind of blew up.


[User] Please transcribe this text

[Assistant] I felt like I saw it coming. There was all this hype and expectation around it. It's finally out. It's going down really well, hasn't it?


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[Assistant] Now it's called the end of everything. Do I then say brackets astrophysically speaking or do I just call it the end of everything?


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[Assistant] And you, you look at basically how the universe is going to end. Is that right?


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[Assistant] This lead, this makes me think about a few things I always think about when I talk to people who do your job. And one is, what does it feel like to know that you're probably gonna be dead when all this stuff happens?


[User] Please transcribe this text

[Assistant] You're probably gonna be dead when all the good stuff happens, all the stuff you think about and write about and research, yet alone the end of the universe. Just, just, you know, things like the end of galaxies and galaxy collisions and stuff, you know, you're gonna miss all that.


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[Assistant] So if I gave you the magic time machine bubble and you could go anywhere forward, back, and also anywhere in space.


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[Assistant] But if you can only go to one place for an hour, I guess you just want to catch it like at its peak. Yeah, yeah. Like what's the night sky going to look like from Earth, oh, there probably won't be an Earth bill there, but what's the night sky going to look like from around here at that point? You're crazy.


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[Assistant] Do you know what, I love space and astronomy, like I really love it.


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[Assistant] But still, if I could have that time machine bubble, do you know where I think I'd go?


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[Assistant] I want to see that moment, what it sounded like and looked like as it hit. Like I'm not happy that the people died and I wouldn't, I don't want to, you know, that's sad. I don't want to see all that, but I just want to see that collision.


[User] Please transcribe this text

[Assistant] I don't think the collision would be, like, as it sank it would be terrible and traumatizing, you know, and what happened afterwards, but just that moment, cause no one, well I guess some people down below deck were hurt when that happened, but the actual collision I think was fairly


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[Assistant] So the Big Crunch doesn't have a dramatic final few seconds. It hasn't, like, the Big Bang has a dramatic start.


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[Assistant] That's, that's gonna look amazing. Yeah. Do you think, like obviously you don't want to be around for that, but-


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[Assistant] Do you think there's any chance, any chance whatsoever, that humans are gonna be around for the finale for as long as life can be around for the finale? Do you think, do you think like our, our future, we have a chance at all?


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[Assistant] So, I mean, obviously the sun won't be around for the end. Does the Milky Way make it to the end or does the Milky Way turn off before the end as well? Like, do we run out of gas and stars here?


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[Assistant] I don't know much about this vacuum decay cause my, the next question, one of the final questions I wanted to ask you is, is there like a universe equivalent of, you know, the asteroid that came out of nowhere and just whacked you in the face, the thing that scientists can't predict? Is that what vacuum decay is?


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[Assistant] So it could have already happened like, so far away and be coming towards us without us knowing?


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[Assistant] Well, on that note, I feel like I better get to work editing this podcast, cause, uh.


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[Assistant] Well that's all for now. You can learn more about Katie's work, her tweeting, and perhaps most importantly, her doomsday book in the notes for this episode.


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[Assistant] Thanks again to G Research for supporting this podcast. They're also in the notes. And yes, thanks to MSRI, the Mathematical Sciences Research Institute for supporting Numberphile. I'm Brady Harron, and you've been listening to the Numberphile Podcast.


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[Assistant] No, I don't think I knew what I wanted to be at all when I was at school. I kind of drifted into physics because I found it quite easy, I suppose.


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[Assistant] Choose what I wanted to study at university. Physics just seemed like a very natural choice.


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[Assistant] I think there was a lot of pressure for us to decide upon our career and I was still very, very uncertain about what I wanted to do until I got to third year and I took part in something called the Undergraduate Ambassador Scheme.


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[Assistant] I loved sharing science ideas with the students at the secondary school. I loved how it was a very active thing to be doing. Yeah, I decided I'd, I really want to be a teacher when I graduate.


[User] Please transcribe this text

[Assistant] I'm joking, and I'm not even sure if I'm that fun. Uhm, what I try to do...


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[Assistant] Is I quite myself, I quite like thinking things through a lot.


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[Assistant] And perhaps including a little bit of philosophy as well. So when I teach I'm very eager to.


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[Assistant] Draw ideas out of the students and have a lot of discussion with.


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[Assistant] And I like that sort of theatrical way that you can perhaps build a bit of suspense. So rather than just telling the students, you know, here's what Rutherford discovered about the atom. I like to try and turn it into a bit of a story. That's what I hope my students would say.


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[Assistant] Absolutely right. Maths is crucial for physics. You know, it's always said that maths is the language of physics. So although I didn't find that maths came easily to me at all, and so I had to do a lot of work and


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[Assistant] That I think came as a bit of a shock to me when I was 16 years old because up to that point in school.


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[Assistant] I think I'd found quite a lot of things not too difficult, except for foreign languages, which I was really, really, really bad at. So I just had to do a lot of work. I remember sitting for hours and hours doing maths homework and then 10 minutes doing physics homework.


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[Assistant] That's a good question. How did music become part of my life? So...


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[Assistant] When I was a kid, my mum, I think, tried very hard to encourage me to learn an instrument. So when I was six years old, I played recorder and when I was nine, I played the violin, except I didn't really play either of those instruments because


[User] Please transcribe this text

[Assistant] I didn't have any internal motivation to practice and I gave up pretty quickly. But then when I was 13, I signed up for something called Duke of Edinburgh.


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[Assistant] Uh, the Duke of Edinburgh award is like, like this scheme that, um, encourages young people to get involved in lots of different activities. And the reason that I wanted to do Duke of Edinburgh was because of the expedition part where basically you get to go camping across the countryside. And to me, that sounded like a lot of fun.


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[Assistant] But the problem was you couldn't get the award if you just did the camping part. You also had to do a community element, which was like volunteering and helping out somewhere. You had to do a sport, which luckily I had covered. I'm not a sporty person at all, but I did.


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[Assistant] I happen to play this quite obscure sport, so that wasn't a problem.


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[Assistant] Hang on, what obscure sport do you play? I don't play it anymore actually, but uhm.


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[Assistant] So the sports, I don't know if you'll have come across it Brady, it's called goalball. It's a sport for blind people. And the ball has a little bell inside so that all of the players can hear where on the court the ball is. I have seen that played.


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[Assistant] Yeah, I, I played that when I was at school. I was okay for the sporting element of the award. The tricky part was the skill where you had to provide evidence that you had acquired some skill. And my sister was already having piano lessons and I thought, okay, I might as well.


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[Assistant] So I went along to this lady whose name was Mrs Cooper, and she seemed to teach everybody in my sort of local area of town. I think Mrs Cooper was probably a little bit intimidated by me as a student. Not because of my personality, but I think the normal way


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[Assistant] Children is that alongside that they learn how to read sheet music and I wasn't able to read sheet music because of my eyesight and so


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[Assistant] Mrs Cooper had this student and yet had no idea how to, how to teach me, really. But she was very, very patient and she was very, very kind.


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[Assistant] And I went to her for three years learning piano.


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[Assistant] Yeah, absolutely. I think there are so many advantages to being able to read sheet music, uhm, the ability to be handed a piece of paper, sit down at your instrument and just play what's written. I would love to be able to do that.


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[Assistant] Um, and I really admire musicians that can do that. The way I had to learn was purely by listening and then copying. Um, so playing by ear.


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[Assistant] And of course, the best musicians in the world can also do that. They can just hear a piece of music and then reproduce it on their instrument.


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[Assistant] That was my only option. So the process was, to begin with, it was very laborious. Uhm, I remember, you know, Mrs Cooper would play me.


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[Assistant] One bar of music. Which might be...


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[Assistant] That's a great question, uhm, yes, I-


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[Assistant] I think in a way it has been an advantage because I'm very, very dependent on listening, obviously, like any musician is, uhm, but for me,


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[Assistant] When I play with other musicians, for example, they might be reading from sheet music and I've, I had to learn how to fit in with a band.


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[Assistant] And I was really lucky growing up and when I went to university that there were lots of musicians around me. And so I had lots of opportunities to play with other people. And it meant that if I had a melodic idea in my brain, like a little tune, then I would just be able to perform that.


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[Assistant] If you have a thought in your brain, you're able to speak that thought out loud without needing to think about it too much. So when it comes to composing, I feel like I do have, uhm, not an advantage because I'm certain that other composers do this as well, but if I have an idea for a tune, then I can immediately


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[Assistant] Kind of get that out of my brain and onto the keys of the piano without


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[Assistant] Spending ages and ages trying to figure out the idea in my head. Super. I don't know if that makes sense.


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[Assistant] Yeah. So when I was learning piano, I didn't have any means of recording anything. So anything that I did compose and I did try to start composing when I was quite, I wouldn't have been as pretentious to call it composing, but I had certain melodies that would just stay in my brain. Um, so I never had to write them down. I never had to record them.


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[Assistant] Um, of course now with, you know, software like Audacity, which you can get for free. Yeah. I'll just record if I have an idea. I've got a little dictaphone as well that I carry around. So if I have an idea for a tune, I'll just, you know, get the dictaphone out and sing into the dictaphone.


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[Assistant] Yeah, I feel very lucky. I have, I have lots of ways that I get to play live music. Uhm, I play percussion for two choirs, the West End Singers and the Southampton Gay Men's Chorus. Uhm, are both fantastic community choirs and I play percussion to accompany them.


[User] Please transcribe this text

[Assistant] I also play at my church, not recently of course, because of lockdown, but before then, every single week, uhm, I'd either play piano


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[Assistant] Or guitar or percussion. And I feel like I'm very lucky at the church because there are some incredible musicians there. A professor of jazz.


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[Assistant] the university, um, near the church and he, he makes me feel ashamed. You know, every time he sits down, every time he sits down at the piano, I'm, my mind is blown by his ability and for a very long time I pretended


[User] Please transcribe this text

[Assistant] That I couldn't play piano or I didn't want to play piano in front of this guy because he was so, so good and I just stuck to playing percussion which is much easier.


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[Assistant] Did he give you the thumbs up when he finally heard you play piano? He thinks you're good enough? He, he, he is a lovely man and he was very, uh, very gracious when he described my piano playing. He said that I had a very lyrical touch. Oh, nice.


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[Assistant] Yeah, thanks. So there's an album called Tuplets for Toddlers, which I've helped to kind of coordinate.


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[Assistant] Yeah, so I've got two small children. My oldest son is four and a half and he's just started at school and my youngest son is one and a half.


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[Assistant] And they absolutely love listening to music. We have music on just all the time in the house


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[Assistant] I play the music, yeaah, uhm, they play music, they've got loads and loads of toy instruments, we've got Spotify on, we've got music in the car, just so much music in the house. And some of the music they want to listen to, I find very tedious.


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[Assistant] You know, nursery rhymes, there are hundreds and hundreds of nursery rhymes available to listen to on Spotify, but...


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[Assistant] After, you know, the 50th time of the Wheels on the Bus, you get a bit, a bit bored, and so at the start of lockdown, I was kind of going a bit crazy listening to the same songs on repeat, and I thought, actually,


[User] Please transcribe this text

[Assistant] I could record some nursery rhymes, but I could make them a little bit different.


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[Assistant] Recording my ideas and my main kind of guiding principle was I wanted the tunes to be recognizable. So just traditional nursery rhymes, but I wanted to do something playful with the rhythm.


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[Assistant] I wanted to have some unusual timing going on that you don't often hear in kids music and in fact you don't often hear in, you know, pop music on the radio.


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[Assistant] I did, I did about 12, um, recordings of my own where I was just experimenting with some new software that I'd got, which made it very, very easy to adjust things like the rhythm of a performance.


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[Assistant] And in fact, it felt like cheating because what I was able to do was just play the wheels on the bus normally, and then in the software I could move the individual notes to produce a rhythm that I hadn't actually performed.


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[Assistant] I really like that analogy. That's an amazing analogy with Shrek. I think what I want to be able to say is that yes, I'm doing it for the adults and maybe


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[Assistant] Particularly, uhm, adults who are themselves musical might appreciate some of these rhythmic ideas. But there is another purpose as well.


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[Assistant] Which is when you hear something, uh, new in music, sometimes that can have a really big impact on you. Like it might be just the sound of a particular chord. And I, I remember this from when I was a kid, just hearing.


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[Assistant] I had some idea in a piece of music and it would really stick with me and I'd wonder like...


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[Assistant] What's going on in that song? Why does that sound so good or why does that sound so sad?


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[Assistant] And so with this Tuplets for Toddlers album, my hope is that...


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[Assistant] Somewhere, maybe even subconsciously, a kid is gonna listen to some of these rhythms and think,


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[Assistant] Oh, that rhythm doesn't sound like what I'm used to. I wonder what's happening in that song.


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[Assistant] That's a great question as well. I think at that age it will be subliminal and I don't think they would be conscious that there's something slightly strange about the music they're hearing.


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[Assistant] As you get older, you might be able to articulate that thought better in your brain and then my hope would be that when adults listen to this music,


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[Assistant] They would recognise that there's something a little bit unusual about it, even if they don't know technically what's going on.


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[Assistant] Well, like this sounds quite arrogant, but it occurred to me that...


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[Assistant] The idea of this album, I'd, I'd never, I'd never come across this idea before, like an album for children that is going to introduce them to some exciting rhythmic ideas. And I already had the name for the album, Tuplets for Toddlers in my head, and I thought,


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[Assistant] What is a tablet? Ah, we'll get onto that Brady. We'll come to that. Okay.


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[Assistant] I had the title for this album, Tuplets for Toddlers, and I thought


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[Assistant] Proper composers, professional composers might kind of get the idea and might be quite excited by it.


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[Assistant] And one thing that I thought might have the appeal here is, uhm, the tunes already exist, you know, the wheels on the bus melody. I think everybody knows that. And so the composer's job.


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[Assistant] Is going to be much narrower. Their task is to take this well known tune and then do something fun with the rhythm. So I contacted David Bruce.


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[Assistant] And he's a composer who has done a huge amount of work. He's had his work performed at the BBC prom and I thought I was probably shooting quite high.


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[Assistant] Then I started contacting other composers. David Bruce has collaborated with some other musicians before.


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[Assistant] On composition projects. So I thought, well, the logical people to contact is, is, yeah, these, these other composers and it kind of went from there.


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[Assistant] I must have contacted maybe about 30 and 10 of them have contributed to the album.


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[Assistant] So uhm, another purpose of the album is I thought it would be really appropriate if all of the money raised from the streams and the downloads were to go to charity and the charity that we've chosen is Save the Children.


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[Assistant] So I think to be able to understand why some of the ideas that the composers have used are so clever is you first of all have to have a basic understanding of how most nursery rhymes are counted. So the fundamental idea here is counting along with the music. So.


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[Assistant] I'll play an example of a typical nursery rhyme and how it would typically be counted. So the nursery rhyme is Frere Jacques and it's counted in four like this.


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[Assistant] Well, let's listen to what that sounds like, and there's gonna be something a little bit off if I try counting to three. One, two, three, one, two, oh, oh, I can't even do it!


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[Assistant] Hang on, hang on, hang on. It's so difficult. The reason that we count to four is this musical phrase, this, it's like a, it's like a, like a sentence.


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[Assistant] That is a little parcel of time and the way that it's most logical to count it is by counting up to four.


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[Assistant] In, in simplistic terms, you can play a note that is the duration of a count of one. You could play notes that last for a count of two. You could play notes that last for a count of three or four, or you could subdivide that count into halves or into thirds. Now to explain why.


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[Assistant] Some of these tracks are so clever with their counting. I'd like to use Frere Jacques again, but this time I'm going to count up to eight. To count up to eight, I'm going to have to count twice as fast, like this. One, two, three, four, five, six, seven, eight. One, two, three, four, five, six, seven, eight.


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[Assistant] So the composer David Bennett has arranged Frere Jacques, but with a count of seven. Now seven, it's an odd number and it's a little bit odd in music as well. Um, I cannot think of the last time I heard a song that was in seven on the radio. What David Bennett has done.


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[Assistant] Is to take this Frere Jacques and perhaps imagined that it was counted in eight, like I just did, but then chopped off the last eighth.


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[Assistant] So if I count along, it would sound like this. One, two, three, four, five, six, seven, one, two, three, four, five, six, seven, one, two, three, four, five, six, seven, one, two, three. Does that sound...


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[Assistant] Yeah, I think that's a great way to explain it. They are, they are packed together and it's a little bit uncomfortable because it's not, it's not what you're used to hearing. It's not what you're expecting. If I, if I don't, if I don't count with it, it sounds like the whole thing is rushing. It's kind of skipping ahead a bit.


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[Assistant] Because what he's doing is he's taken wind the bobbin up, which is normally a count of four, and he's going to count up to eleven.


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[Assistant] Now, I, I don't know what David Bruce's compositional process was, but the way that I understand what he's done is he's taken, wind the bobbin up in four and then re-imagined it in six.


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[Assistant] Can I play you what that might sound like? Can you play it to me normally first as a four? Of course, I'll play it normally in four.


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[Assistant] One, two, three, four. One, two, three, four. That is very, very standard for a nursery rhyme.


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[Assistant] Like I say, I don't know how David Bruce imagined this as he was composing, but one way perhaps to understand it is take that same tune


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[Assistant] But now, let's have an underlying count of six, like this.


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[Assistant] One, two, three, four, five, six. One, two, three, four, five, six. Now, already, that's a little bit odd for a nursery rhyme. You don't hear many nursery rhymes with that kind of count.


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[Assistant] But now imagine that we double the rate of counting to 12. So something like this.


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[Assistant] I'm not going to be able to count along with that Brady because I'm concentrating too hard, but I'm, but I'm playing with my left hand twice as many notes. I played 12 notes in total. Now what David Bruce has done is to cut off that last 12th.


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[Assistant] And the effect is, to me, when I first heard David Bruce's submission, it just made me laugh for joy.


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[Assistant] Not laughing at it, but just laughing, appreciating how it transformed this very, very normal nursery rhyme into something very peculiar indeed.


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[Assistant] Quite a few of the other composers, they've also taken this idea of


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[Assistant] Taking a normal count of four and maybe adding to it or subtracting from it.


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[Assistant] So I've played all of the songs to my two sons and their favourite one by far is the one that Ben Levin has done, which is B-I-N-G-O.


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[Assistant] And what Ben Levin has done is to count up to five basically. And yeah, that's, that's odd to have five underlying the music, but it's, it's there throughout the piece. I cannot sample what Ben Levin has done because he is a creative genius and.


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[Assistant] The only way to fully appreciate why it's so good is to listen to it. Okay, let's have a little listen.


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[Assistant] Amy Oltie is another composer who's contributed to this and what she's done is kind of the same as David Bruce in that you could count along with her London Bridge by counting up to 11.


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[Assistant] Actually, when you listen to it, it's far, far more logical to count six, five.


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[Assistant] And then five, six. Ah, so changing the count during the song. Exactly. So we're, we're kind of cranking up the, uh, complexity level here by having the count changing.


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[Assistant] Now, 12tone, who is another composer on the album, has taken this idea of changing the count, and he's taken it to an extreme. Can I read out?


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[Assistant] The counting that is required for Twinkle Twinkle Little Star. Of course. I don't know how interesting this would be to listen to on a podcast, but I don't know. Okay. So in Twinkle Twinkle Little Star, in order to count along successfully, you need to count three, two, three.


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[Assistant] Two two three, two two three, two two two, three two three, two two three, two two, three three three, two, two three, two two three, two two three three, two two one.


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[Assistant] Two three, two two three, two three, two two three, three three, two three, two two three, one.


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[Assistant] How, how, in fact Brady, how do you know Brady that I haven't done it in a Numberphile video?


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[Assistant] So, so yeah, Twinkle Twinkle Little Star takes the idea of counting and it just pushes it as far as it can go and it's like


[User] Please transcribe this text

[Assistant] When I heard Twinkle Twinkle Little Star, immediately I felt like it was a challenge. Like I wanted to be able to count along with this music.


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[Assistant] And, you know, I'm not ashamed to say it took me about probably 20 minutes to be able to nail down exactly how this music has been counted. It's just so...


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[Assistant] The quintessential tuplets on the Tuplets for Toddlers album have been performed for us by Sean Crowder, a jazz and electronic drummer. And I think being a drummer, perhaps he has got


[User] Please transcribe this text

[Assistant] So when you first start listening to Sean Crowder's Itsy Bitsy Spider, you'd be forgiven for thinking that it's a count of four.


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[Assistant] Because he, he even starts the song by clapping one, two, three, four.


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[Assistant] And you could probably listen to the whole track and not even detect that anything strange is happening at all. And I think I can say that with confidence because when I first heard this concept of tuplets in a song,


[User] Please transcribe this text

[Assistant] I couldn't recognise, like, my brain wasn't wired to be able to identify


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[Assistant] So Brady, for It's a Bitsy Spider, I've sent you a clip of me counting along to it. And I think what makes this special is the speed at which I have to count. Because what Sean Crowder has done is to take these regular beats. One, two, three, four.


[User] Please transcribe this text

[Assistant] And he subdivided them into tuplets.


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[Assistant] A tuplet is when you take a beat and you cut it up into equal duration segments, but


[User] Please transcribe this text

[Assistant] The number of segments that you cut it into is, in some way,


[User] Please transcribe this text

[Assistant] Uh, unusual. And so what Sean Crowder's done is to cut it into five.


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[Assistant] And when you cut a beat into five, that's known as a quintuplet. Counting along to quintuplets is not easy. Physically vocalizing the count requires practice. And you'll hear it in the clip, but the way, the way that some drummers count this is they count one tiki taka, two tiki taka, three tiki taka, four tiki taka.


[User] Please transcribe this text

[Assistant] It's quite an unusual idea to use quintuplets and it's very difficult to find songs that use quintuplets. It is possible and increasingly musicians are starting to incorporate these into their songs.


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[Assistant] And my hope is that if little children get to hear quintuplets at a young age, they're going to be.


[User] Please transcribe this text

[Assistant] Ready or at least better prepared than most grownups are for understanding what's going on.


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[Assistant] Yeah, uhm, it's exposing them to something that they probably wouldn't hear unless they went searching for it. And I'm not sure how many toddlers are au fait with the Spotify interface.


[User] Please transcribe this text

[Assistant] That, yeah, that's a great question. So why hasn't someone done this before? I think the reason...


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[Assistant] Another reason I think is that psychologically and physically some of these rhythms are very difficult to perform and later on I'll get onto polyrhythm which is where you're counting


[User] Please transcribe this text

[Assistant] There is something slightly uncanny about some of them, perhaps because we're so conditioned to hearing songs that have this counting scheme of four, that whenever we hear a different counting scheme, something in our brain says, Ooh, that's a bit odd. Like literally odd.


[User] Please transcribe this text

[Assistant] I think it's got this added layer for all of the mathematics nerds and all of the music nerds that we've got some really complicated stuff going on under


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[Assistant] You know, I haven't wanted to play this to loads of people because of course these composers have sent in their work and it's kind of, you know, it's, it's a project, it's in progress.


[User] Please transcribe this text

[Assistant] And so it's really interesting, Brady, to hear what your reaction to it is. And I don't mean this at all offensively, Brady, but as you've said yourself, like, you don't have loads of musical training, and so it's particularly interesting to hear what your impression of it was.


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[Assistant] All of the tracks so far have involved taking a familiar tune and changing the underlying counting scheme.


[User] Please transcribe this text

[Assistant] In Three Blind Mice, which is the one that I did, what I've done is something called polyrhythm.


[User] Please transcribe this text

[Assistant] So there are actually two counts going on at the same time. With my left hand, I'm counting up to four and that's four equal divisions of time.


[User] Please transcribe this text

[Assistant] And with my right hand I'm counting up to three, but the important thing here is that my counting to four and my counting to three are taking the same period of time. So with my right hand I'm having to play slower.


[User] Please transcribe this text

[Assistant] It's a nice device and some of the composers have taken this idea of counting to different numbers and they've really gone to an extreme. So in Row Row Row the Boat, there are four different counts running simultaneously by the time you get to the end of the


[User] Please transcribe this text

[Assistant] Wow. And I would challenge anyone to figure out what those counts are. They're whole numbers, but, uh, yeaah, it's good fun to listen to that one.


[User] Please transcribe this text

[Assistant] Row Row Row the Boat was by 8-Bit Music Theory. London's Burning.


[User] Please transcribe this text

[Assistant] Taking this idea of perhaps different parts, different instruments that are all playing the same tune, but counting at different rates. So London's Burning uses a very, very old technique called mensuration canon.


[User] Please transcribe this text

[Assistant] Menstruation canon was very popular in the 15th and 16th century.


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[Assistant] And what composers like to do with it was kind of show off their mathematical prowess by following some very strict rules and then creating music that sounded nice.


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[Assistant] Can I, can I explain what the rules are in menstruation canon? You can try.


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[Assistant] I can try. So in, I'll simplify it. In London's Burning, which is a great example for this, there are basically three different lengths of note. There are short notes, there are long notes, and there are very long notes.


[User] Please transcribe this text

[Assistant] Now the long notes are twice as long as the short ones and the very long notes are four times as long as the short notes. And that's the way that London's Burning would normally be played in a ratio of one to two to four.


[User] Please transcribe this text

[Assistant] In the version that's on tuplets for toddlers, we've got four different instruments and they're all playing London's Burning, but the ratio of the note lengths is different for each instrument.


[User] Please transcribe this text

[Assistant] Can I, can I tell you what the ratios are? Go ahead. This one has been arranged by Sam Shackleton and what he's got is the clarinet playing the normal tune in a ratio of 1 to 2 to 4.