What songwriting has to do with learning math

Vanessa Vakharia 0:00

I see the way you're acting like it makes me frustrated. You crawl and you go like, what are those words?

David Kochberg 0:08

Is this how we're starting the episode? I guess so. Hey, welcome to Math Therapy. We're talking about songwriting,

Vanessa Vakharia 0:15

like I guess we are. All right. So why you gotta go and make things so complicated? One of the greatest songs ever written by Avril Lavigne. Why are we talking about this? Why did I start that way? Am I starting that way? Should I start again?

David Kochberg 0:28

Hey, it's your podcast.

Vanessa Vakharia 0:29

Here's what's happening this week at Math Therapy, which is kind of weird, but I think will make sense to a lot of you who know me. David and I are on a songwriting retreat. In addition to him producing my podcast, we're also in a band and we are writing a new album that we will be recording in a few months. And as the week has progressed, I have noticed more and more that the process of trying to write a hit song is basically identical to the process of trying to solve a math problem and like all of the complicated emotions around trauma and feeling not good enough and feeling stuck and having anxiety and feeling like you need a specific outcome. And so you can no longer focus on the process. Like all of the things we talk about in math education have come up so often this week that I was like. I think we should do an episode about this because musicians and artists are notorious for hating math and having math, trauma and feeling like math has nothing to do with their craft. And I find that mathematicians are notorious for thinking that, uh, creativity and like fluidity are in opposition to logical thinking and reasoning. And I think it's just so interesting because to me, being in both worlds, the worlds are so similar, and the mental processes and the emotional hurdles that we go through when we're either songwriting, doing something quote unquote creative, or solving a math problem, which is also completely creative, but we don't think of it that way. It's all the same thing. It's all the same fucking thing.

David Kochberg 2:05

Agreed.

Vanessa Vakharia 2:06

Now here's the thing. You always hear people say like, but everyone knows that music is math, right? Like people will say stuff like that. Like in the math education world, when if you have like a creative friend or student that's like, oh man, like I'm not interested in math. Like I just wanna be a musician. Like our go-to is to say, but music is math. And I actually wonder if,

David Kochberg 2:27

but nobody buys that. No one. You say that all the time.

Vanessa Vakharia 2:30

I say it all the time. But,

David Kochberg 2:31

and then ev, anyone who. Would disagree would be like, what are you talking about? That doesn't make any sense.

Vanessa Vakharia 2:35

It's true. And you guys probably know this story that's in my book Math Therapy about our guitarist, Eric, and how I try that technique on him. Mm-hmm. And it did not work until it did whole. Other story we won't talk about. Now here's, here's the thing. When people say music is math, there are so many ways in which it's math. I don't know what people are talking about because everyone's talking about a different thing. But what they are usually talking about is. Notes and patterns and music, they're usually talking about that. That could be a whole other episode. But today what I actually want to talk about is how the process of writing a hit single is the exact same as the process of solving a math problem.

David Kochberg 3:18

Whoa.

Vanessa Vakharia 3:19

That's what I wanna talk about.

David Kochberg 3:20

Whoa.

Vanessa Vakharia 3:21

The process.

David Kochberg 3:22

Yes,

Vanessa Vakharia 3:22

the, and we're gonna talk about three key, because there is so much we could talk about,

David Kochberg 3:27

well, that music is math thing. I think that that the reason someone who will have the initial gut reaction of, I hate math, they would just not buy it. Because I think the narrow definition of what math is right, is what most people are very. Like we all, everyone's got people like this. Probably listeners are like this. Like I can think of people in my family or people you've talked to on the podcast, um, that are, are just. Math is one thing. Math is just, if it has numbers, it's math.

Vanessa Vakharia 4:01

Yeah.

David Kochberg 4:01

So if you're saying music is math, like sure, there's numbers like time signatures and stuff, but that's pretty in the weeds. Yeah. So like no one who doesn't know anything about music yet is gonna know that there actually is number math, but it's, that's their, the only way that they're evaluating is something math. But what you're trying to say is that actual. Actually patterns and structures.

Vanessa Vakharia 4:23

You know what I'm, it's true, but I'm not even saying like that. I am saying that, but that's a different conversation. I'm saying that mathematical thinking is the same as creative thinking. Like I, I I'm saying that mathematical thinking is the same as pop sensibility. Whoa, there you fucking go. Yeah, that's what I'm saying.

David Kochberg 4:44

Okay. That's what I'm saying. Yes. Okay, so this, so this episode you will. It elucidate how? Mm-hmm. I don't know if that's the right word, but how I don't, mathematical thinking doesn't necessarily just have to be what would traditionally be called math and how, and you're illustrating that through creative thinking.

Vanessa Vakharia 5:06

Yeah, but even now there's already a problem because

David Kochberg 5:09

I'm doing a bad, I was trying, it's not your problem. I was trying to summarize your intro and like put a punctuation on and I ruined it. I guess

Vanessa Vakharia 5:15

if you didn't ruin it. It's just, I think that, that we're, we're, we're getting to the crux of the problem, which is all of these language choices, like we're gonna show how mathematical defining our terms, right? Like how mathematical thinking is creative thinking. Yeah, those are the same thing. We're not gonna show how one is the other. Like they are one and they're the same thing.

David Kochberg 5:31

Okay. Forget what I said. Maybe I'll just cut it out, but no, we're gonna No, no, no, no, no. Keep it in. Okay. You say the next thing you were gonna say,

Vanessa Vakharia 5:37

I think, I think this is what I want the crux of today to be is whether or not you, because most people listening to this are probably not songwriters themselves. So if you listen to music, period. This episode is for you, like if you listen to music and you hate math. This episode is for you if you love math, but you're like, I don't really care about music that much. This episode is for you. The whole point of this episode is to show that mathematical thinking is not confined to a math classroom. And mathematical thinking doesn't mean that you have to ditch creativity. the reason this all started is because I told you guys at the beginning of this episode, probably once every two years, me and David go on a songwriting retreat. It's not that we won't write songs in between, we do, but mostly we save like an album cycle for the bulk of the songwriting, which means it has now been months and months and months since I've written my last song. Now. Very similar to math. If you don't use it, you lose it. But it also is like riding a bike, right? So we get back into our groove here and the first few days I'm really struggling, I'm like, fuck. Like I can't even write a song. I don't even remember how to do it. Like how do I even write a song? And so like, because I'm desperate and I'm like, we need to produce songs like we are recording this album. Like I'm feeling all the pressure. I start being like, okay, what techniques do I have? What tools do I have? What can I draw on? Now I want you guys to keep in mind, we've been in this band for 14 years, and David can attest to the fact that I've written songs in a bajillion ways.

David Kochberg 7:10

yes, I've

Vanessa Vakharia 7:10

written songs by humming a melody. I've written songs by picking up a guitar. I've written songs by picking up a piano. I've written songs by just. Se writing a bunch of words and you know, and then David will take them and do something with them. There's all these ways, but in my desperation, after the first few days feeling like, oh my God, I have writer's block. I don't know how to do this anymore. I don't know how to write a song. And the pressure of being like, we need to write a song or an album with all these songs, like albums are super expensive. Like, I need to like make this worth it. I. Went to one of my tried, tested and true methods, which is I get a backing track. Okay? So I'll download an instrumental track off of the internet. And I will write a melody to it. I find that really the most simple thing for me. Sometimes, so, right, like I have this instrumental track. I'll start humming along. Words will come to me, whatever

David Kochberg 7:57

This is called top lining in the, uh, parlance of the songwriting game.

Vanessa Vakharia 8:03

It's called Top Lining. So what'll happen is I'll get this backing track. I'll write a melody to it and some words. Then I'll play it for David with or without the backing track. And he will write a brand new backing track. Sometimes we'll change it, well, we will change it completely. Sometimes it'll have a different vibe. But the point is that that backing track inspires me. It It gets me thinking creatively, and it lets me let go of the reins because I'm not starting from scratch, it's a tool I use. Now, David, however, a few days ago. Kind of frown down upon this. Would you like to throw that in here?

David Kochberg 8:37

Frowned down is a loaded tur.

Vanessa Vakharia 8:42

But you were, you were kind of having a bit of an attitude about it.

David Kochberg 8:45

I was having an attitude about it, but it, it was more in the context of you being insistent that that's the, that was the only way that you could write at that time. I, I don't, I I think it's a valid for sure, it's for sure a valid way to write songs because you've written lots of our songs that way. So I don't have any problem with it exclusively. It's, it's just that you were, because of the, the state you were in and kind of the low confidence in yourself, I just was taking issue with the kind of stubbornness of. I was just trying to help like gas you up and break you outta your funk. And I was trying to encourage you to remember, you can do all of these different things, but you were like, right now the only way I can write is such and such. Okay. That was more so,

Vanessa Vakharia 9:38

so you didn't like that, I was like being insistent that I needed this tool to write

David Kochberg 9:43

Kind of. Okay. However, I also recognize like if you, if one is in a zone of low confidence, then it's hard to just inspire yourself to act normal. And so it is good to use a tool. I think it was, there was just a lot of cross wires, like broken telephone between two people in the same room.

Vanessa Vakharia 10:01

Okay, well let's not, let's, I don't wanna, yeah, just get in the weeds, right. We don't need to get into the weeds. My point you brought up, my point is that I wanted to use this tool. Yeah. Okay. So let's look at it this way. 'cause I want us to start thinking mathematically. I wanted to use this tool. Okay. The tool, in my opinion, did not hinder my creativity. It helped my creativity. It just gave me something to work with, and then the result is a great song regardless of how I wrote the song. The result is, it was, I wrote a great song. Now, hold on. One more thing I wanna say here is. You a part of what you had said during that time. I know your opinion's a bit different now, but David had the stance of being like, well, I just think like you were kind of saying like the, the. He was kind of being a purist about it, right? He's like, well, I just think like the coolest thing, like the, the highest level of songwriting is if you come up with something from scratch.

David Kochberg 10:54

Sure. I think what, I think you're kind of combining a few different conversations into one, but that is, but that, let's roll with that. So, yes, I, I was arguing broadly about some kinds of tools where one can rely on those tools. Either first or very early on before giving yourself a chance to come up with something new yourself I think what you're trying to talk about is maybe what we, what I was saying just about like a rhyming dictionary or a thesaurus or chat GPT or if you're like, let's say, I wanted to write a song about my favorite mathematical theorems. Okay, great. And I was like, oh, Pythagoras Pythagoria theory. Py. What's it? Pythagoria? Low floor, high ceiling. Yeah, sure, sure. Fermat's. S uh, something Fibonacci. And then, so we just write things down for 30 seconds, and then we hit a block, and then five seconds goes by and we're like, uh, let's just look on ChatGPT. Bt like, suggest me some theorems that I could put into a song. So my point was more about something like that, where instead of giving yourself the time to sit with the discomfort of not knowing where to go next. And then pushing through that and then discovering somehow within yourself, maybe you have like a new idea that pops out. Maybe it takes a few minutes of like having a blank canvas and you're not sure, and then something pops to you. Giving yourself that time allows for creativity to pop out as opposed to if you, just very quickly when you don't know the answer. Immediately go to, like someone else kind of suggests some answers to me, the purest part of it was that I would rather if, if the end result is to have a smash hit about mathematical theorems, then I would rather that those had just come from our collective creativity and experience that came out as a result of the writing experience and project. As opposed to, we just got AI to summarize a bunch of them, and then we're taking those and like organizing them into a song. It's less creatively, artistically satisfying to me.

Vanessa Vakharia 13:06

Okay. You've, this is really good. 'cause you've said a lot of good things. You, you've honestly, well, a lot of things that are just, it's, it's all the conversations we're having in math education. Hmm. Because first of all, it's really interesting that you ended on being like, but it would just be more satisfying to me if I had come up with it. Result versus process. That's what we're talking about. We're saying regardless of the outcome, the process matters. Yeah. Now, now here's the, the big problem though is it's so subjective. So what you're talking about, that idea of instead of going to the rhyming dictionary right away, right. We're writing the song about mathematical theorems. For whatever reason, we spend 30 seconds just riffing on our favorite mathematical theorems. Mm-hmm. We then get stuck. We can't think any of anymore. We go to chat GBT and ask for some. Versus we're writing a song about mathematical theorems and we just start without even thinking about it. We're like, chat, just suggest some we're talking about, right? Like those two things. So what we're talking about. Mm-hmm. And this is really interesting because the cut just wrote an article introducing a term called Friction Maxing. And. I'm obsessed with it because the, the whole thing, what it's basically saying is it's made up this term friction maxing. And what is it is, is increasing the tolerance for inconvenience. Whoa. Increasing the tolerance for inconvenience. And the example I gave was exactly what you're talking about. Like you're writing a song, you need to write an email. Instead of going to ChatGPT right away try to spend 10, 20 minutes writing that thing that you're stuck with without cha g bt. So I guess you're maximizing the friction. I don't know. Whatever. And then you can go to the tool. So all of a sudden your window for tolerance for inconvenience becomes larger. Like you're able to sit with it more. This is exactly what we talk about when we talk about productive struggle in math class. Hmm. Is the exact same thing basically. Right? It's like so great. They've made up this whole new term actually really like friction maxing kind of sounds cooler than struggle. Cool rebrand. Friction maxing. Friction maxing. But I, but, and also I like, I like that, uh, call to action

David Kochberg 15:09

sounds like a competitive sport.

Vanessa Vakharia 15:11

Mm, totally. Like you're getting shredded, like your brain's getting shredded. You're like, and also just the idea of like increasing the window of tolerance for inconvenience seems like actually a very practical, uh, thing to do. Inside and outside of the classroom, like you need to do that in life. You need to increase the window of tolerance for inconvenience and productive struggle anyways is the exact same thing. It's the idea of let kids struggle because when you struggle, when you increase the window of tolerance for inconvenience, what will often happen is. You will, like you said, have this moment where you're like, oh my God, wait a second. I know how to do it. Or, or you'll, you think you're stuck, but when you push past that, something will come up. Like you'll remember something from the past. You'll try something new. And then this leads to your last point, which is the satisfaction you get when you get an outcome that way versus just asking someone else for help or looking it up on ChatGPT, that satisfaction. It's not just satisfying, it's empowering. Because all of a sudden you have ownership over that outcome. And when you Yeah, it's

David Kochberg 16:13

a real sense of accomplishment. It's

Vanessa Vakharia 16:14

a, well, yeah, but not only is it a sense of accomplishment mm-hmm. It, it literally leads to more confidence the next time you're faced with a problem.

David Kochberg 16:22

Okay. Yeah.

Vanessa Vakharia 16:22

Because now you're like, but I did that last time. This is why I think it's so important for us to be talking about outcome versus process and math for so long has been outcome oriented. We just want the answer like, fucking just get the answer.

David Kochberg 16:36

Yeah.

Vanessa Vakharia 16:37

But when you do that, especially in today's world, we're now screwed because if you wanna just get the answer, if that's your goal, you can do that with, with by barely thinking at all. There's all sorts of resources you now have.

David Kochberg 16:49

Yeah,

Vanessa Vakharia 16:49

and same with songwriting. I just wanna tie it together here of if the outcome is simply a good song. I have listened to some AI generated music that was amazing. I did not know it was ai. Mm-hmm. And we, you and I have different lines like you know, you to, you a rhyming dictionary is too far. To me it's not, but writing lyrics with chat, GPT is too far for me. And AI generated music is way too far. Whereas a lot of people listening might be like, I don't care if my music is at AI generated, as long as it's a good song, why would I care? So I think it's all things being equal. If the outcome is to get a good song, if the outcome is to get the right answer, if you're going to do that anyways. Right. You're, you're, that is the expectation. Like I'm not just fucking around with songwriting and top lining being like, well, I don't care if I get a good song. I do care if I get a good song. You know what I mean? But like, I could get a good song. I could just go to ChatGPT. Actually ChatGPT really sucks at songwriting, but like. I could be taking all sorts of shortcuts right now, and I have to decide where the line is on what shortcuts I'm gonna take. I've decided using a backing track will help me. Using a rhyming dictionary will help me. Now I will, I will pause and think, try to think of my own rhymes first, but I have no problem using a rhyme rhyming dictionary if I get stuck. Mm-hmm. But, using the tool of ChatGPT to be like, Hey, I wanna write a song about this. Gimme some, like, I wanna write a song about my ex and how annoying he is. Like, list some, some typically annoying things exes do that is, that's pushing it for me. I'm not gonna feel good if I get a good song that way.

David Kochberg 18:20

Mm-hmm.

Vanessa Vakharia 18:21

Same with math. It's like, no, you, you, you need to get the answer right. But is it gonna benefit you or the process if you got the answer by asking ChatGPT and writing it down or memo, right. Like, or yeah. let's assume you're going to get the answer anyways. That's the goal of it. Then when do tools help and hinder that and how do we treat the process?

David Kochberg 18:45

Yeah. Yeah. Something else that makes me think of is that, that, that furthest extension of this. Idea of, of AI music, just being someone can just go into one of those apps, type in a prompt, say, yeah, make me a pop country song about mathematical theorems and we should do that. And it's like, you can say. With a guitar solo. Yep. And with female vocals and lots of harmonies and, and you just, I mean, that's even more than what people put in. But anyways, you can just type that in and then this program will just spit you out a like beautifully professionally produced sounding fabrication of a song and the average listener will have no idea. Even me, I could listen to it and be like, wow, that sounds pretty good. But, so I think that that is the thing in, in terms of. What is the point of that? Like all this AI slop, like that's filling our world, it's our mindless entertainment. But in terms of talking, if, uh, ideally. Education is about empowering an individual person. There is to feel like, wow, feel like they can learn. Like this is in a, it's maybe naive these days, but you this, you gotta hope, you gotta, you gotta pray for the world where you want kids to go through the education system learning, the things you're teaching them, but also learning how to learn and learning how to be confident in themselves that they'll be able to continue learning through the world and taking on its, its challenges. It presents them. So for, yeah, this is a bit this, this whole thing about being able to just manufacture very complicated things by a prompt is very concerning for everyone because it reduces the human ability, to learn things and figure things out.

Vanessa Vakharia 20:38

This is such a tough one though, because I agree with you. You're like, like, yes, part of the goal of ED education is to empower, right? Like, yes, you're trying to get answers to thing, you're trying to learn content, but you're also trying to learn like the skill of what it means to learn and solve problems, right? Like of your own accord with like with the, the tools you have. But I do think we're there is this fine line because it's like, what is the threshold, right? Like for example, it's like you are saying, yeah, but Vanessa, if you just push through and you thought of your own rhymes, like you, you know, you would, you would eventually move through it. You don't need that rhyming dictionary. And I'm like. Yeah. Okay. I'll, I'll, I think it's important to like try to just like free because the act of freeing your mind enough that you're not so focused on the outcome that you can't get to the outcome. Right? Like sometimes you're thinking so hard about how to solve a problem or how to like make a chorus work. Mm-hmm. You're not gonna get there. So being able to like let go a it and let those rhymes come to you, it's good. But then I'm kind of like, yeah, if I haven't thought of the rhyme in like 30 seconds or whatever, if I'm stuck, I'll hit the rhyming dictionary. But to someone else, they might be like. No, like you're, you're giving in too early. Like what is the threshold? I, I think everyone has to decide, right? Yeah. It's like, and also we're, again, we are living in this world now, right? Where young people have access to these tools like calculators, like ChatGPT, this and that.

David Kochberg 21:53

Yeah.

Vanessa Vakharia 21:54

Part of learning how to learn is learning how to use the tools at your disposal. And I actually don't think it's their fault. Like, it's like, it's like they're trying to learn how to use the tools at their disposal. To get outcomes efficiently. Like they're, they're clever in their own way, right? Because they're like, oh, you know what? I could solve this problem by putting in this prompt. Like, that is a form of intelligence, of course. But, but by doing that, they're now missing out on developing this whole other skill. Sorry, shit. They're missing out on the, on developing this whole other skill, right? Of like.

David Kochberg 22:29

Yeah,

Vanessa Vakharia 22:29

it's, it's really hard because I think it's like who gets to decide what that threshold it is? Yeah. And you know, we talk about this in math, takeaway like artificial intelligence. We actually argue about, not argue, but there's a lot of perspectives on this when it comes to manipulatives in mathematics, right? It's like using, handheld tools, like not even electronic, right, but like arrays or blocks or like any of that kind of stuff. Like there's so many things where I think educators for a long time have split. They have differing views on, some people will say, well, manipulatives are hindering learning, right? Kids need to abstract their thinking like they, and then there will be a whole other grouping, like, but that's a tool they have where they can make their thinking like physical and visual, and some people need that. So it's like. It. I think this is very much like when does the tool hinder and when does it help? Yeah. Because for me, that rhyme dictionary, sometimes I'll be flipping through the rhymes and I'll see a word that I was not even on my mind and it'll gimme an idea for a whole other vert. I'll be like, wait a second. I could like, mm-hmm. Talk about this other thing. Right. But yeah.

David Kochberg 23:32

Yeah. Yeah. I, I worry that maybe this happens every time we talk about AI is that it like meanders and branches off into all these different tangents. So I just worry maybe have I taken us too far off course? Well, let's, the theme of the episode, no, no, because we're

Vanessa Vakharia 23:48

almost, this is now the theme. Like there's Oh, wow. 'cause it all kind of weaves in like the idea of,

David Kochberg 23:53

because initially you were saying how is mathematical thinking similar to song creative songwriting thinking,

Vanessa Vakharia 23:58

right. I don't know. I think the part about like AI music, I just dunno how many people listening to this. I'm very curious if, listen,

David Kochberg 24:07

maybe people don't even know about it.

Vanessa Vakharia 24:09

Well know about it. Or like, I'm actually curious and I want you guys to text the podcast if you care. Would you care if a song you were listening to, if you were like jamming to the song, you were like, I fucking love this tune. And you checked, and it turned out the song was entirely written by ai. There was no humans on it. The vocals are not human. Like, would you care, would it make you like the song less?

David Kochberg 24:30

That's yes. But in the context of this question, it's challenging because that's a, that's a question from the consumer perspective like we're talking about in terms of a, a student learning math. We're talking about. No, but I know how the, the, the shortcut of that it takes to make something or to get to an end result. The question of someone appreciating a song as a listener differently if they know that it was made by a human versus by. AI is a totally different question,

Vanessa Vakharia 25:01

but I actually think it's not. Hmm. Because I think teachers, I think teachers need to ask themselves that. I think policy makers need to ask themselves that. I think administrators need to ask themselves that, but about, about math.

David Kochberg 25:13

About math, do you care? Do you care if your student gets the right answer? But through no real critical thinking, just through basically like outsourcing.

Vanessa Vakharia 25:25

Do you care? And, and if you do care,

David Kochberg 25:28

yeah.

Vanessa Vakharia 25:28

Then we, we need to be asking again, as we keep asking, what is the purpose of math class? What are we really, what are we really trying to get? And is the means and the medium actually getting us there? And if you don't care, like no judgment either way, like, I'm actually just very curious because you will hear these conversations being like, no, like students have to get the right answer and, we just really care about outcome. But also they have to show their work. But you usually, the show their work is like to make sure they're not cheating or they're doing something the way we told them to. But often, like, here's my question to you. Do you care if your student got the right answer? They used the algorithm, you taught them, they followed the steps, you told them, so they didn't outsource it, they actually did that. Mm-hmm. But they actually have no idea what it means. Mm-hmm. And how they got there. Do you care or do you not care? Like I just think it's a good que 'cause I actually think it's quite similar. It's like how much, yeah.

David Kochberg 26:29

Are they gaining a deep understanding of what's going on or are they just. Getting the answer or but following some memorized steps.

Vanessa Vakharia 26:36

Well, and let me take it a step further actually.

David Kochberg 26:38

Sure.

Vanessa Vakharia 26:38

Here, this is this, here we go back on track. This is gonna tie it into the music question about whether or not you guys who are listening care about whether your music is AI generated. Okay. This will tie it together. There's a lot of people saying, math skills are decreasing. Like kids don't know what they used to know, we should go back to teaching math the old way. And one of the arguments against that is, okay, fine, cool, we could, but so many adults we know today hate math. Okay. They hate math, but they do know their timestables. Some of them more than like allegedly. Okay, allegedly. So my question is. Do you care if your students get the answer? They did it. They followed the thing, they, whatever. They know their timestables, but they hate math. Do we care that they emotionally don't feel great about math, but they know how to do it? And I think that ties into the AI song thing because it's like, do you care? I'm really trying to tie it together. Do you care that there is no emotional, there's no emotion or confidence or growth or like anything around the music you're listening to?

David Kochberg 27:43

Humanity. What?

Vanessa Vakharia 27:44

Humanity. Human. The humanity. That's it. Because to me, I'm like, that's where I draw the line. I'm like, I feel like I just, if I knew this song I was listening to and I was like, oh man, I'm feeling it. And I, and I realized it was just empty. I don't know,

David Kochberg 27:56

like AI just made this thing because it's built to predict what a human would make based on what humans have made. This whole conversation is very complex and esoteric and in the weeds and very philosophical. So it is interesting because. That is an interesting question. Do you care if, does a, a student feeling good about math, liking math, does that mean that they understand it? Is, is does it matter? Is a good relationship to math linked to understanding This is what hap this is what's more common in a lot of your conversations on the podcast, what is the connection between a satisfaction with mastery of the deep fundamentals of what you're learning? Compared to just being like, there's also satisfaction in like, okay, I memorized what theorem, what equation to use when, yeah, I don't really understand it, but I can be satisfied by knowing I got the right answer because I did the thing correctly. Even if I don't understand, that is satisfied. That can s that can be good.

Vanessa Vakharia 28:59

And that, and that's again, this goes back to, so this is hard.

David Kochberg 29:03

There's still problem solving on your own accord based on what you have learned. So everyone's. Everyone learns differently. Everyone's got different strengths and weaknesses. What I think with the music thing, I remember when, even when just image generation first spread out all, all over social media, and then you've got people who are posting these things and essentially calling themselves artists. There's all these people who are very adamant about. AI art is the same as human art, and we don't have time to get into all of the issues around that. It's, it's been 35 minutes. That's what happens when we talk about ai. But so the, the idea of someone, if you compare someone not having any musical training or knowledge or understanding of how music works, but you just type into it. A, a program, gimme a song and it spits out a song, and then you say, you're a musician. Oh, I made this thing, you oof, you didn't make it. And then we're, here's the other thing, is the satisfaction of that will be so fleeting. So fleeting, whereas you're not gonna

Vanessa Vakharia 30:07

feel good. Whereas

David Kochberg 30:08

where it, it's just, oh, I made this thing, but you're not gonna go. Perform it at an open mic. You're not gonna go start a band and tour it and record it. Well, it's already recorded, but if you make a song and you're like, this song is part of me and I externalized it and it's something I've made that I am proud of and means something to me. There's, that's so different, and I do think that even on a subconscious soul, whatever level, people can sense the difference. Between that,

Vanessa Vakharia 30:42

that's deep. I, yeah, there's so much, but probably

David Kochberg 30:46

not a conscious level. Not not on unconscious, but

Vanessa Vakharia 30:48

on a soul level. And I think it will matter. Like, I think, but okay. I think we're going too far into this.

David Kochberg 30:53

We that we've been, this is real and this is really, I really wanna

Vanessa Vakharia 30:56

talk about so much more because the, the episode started with should do a part two.

David Kochberg 30:59

Well,

Vanessa Vakharia 31:00

do you guys wanna a part two? Like is this too much? Like, I feel like we're really, like they can't

David Kochberg 31:05

answer right now. Can

Vanessa Vakharia 31:06

you guys text us and you want, because what I want this started with, how is writing. How is mathematical thinking the same as pop sensibility? Part of it is this. Hmm. Right. Part of it is everything we're talking about, but there's a whole other part, which is about the formulaic nature of writing a song.

David Kochberg 31:21

Mm-hmm.

Vanessa Vakharia 31:22

And how,

David Kochberg 31:23

yeah, that's the whole point we were gonna talk about is there actually is so much math. We didn't even talk about Amy Allen.

Vanessa Vakharia 31:28

Yeah. We didn't even talk about Amy. Here's what we do.

David Kochberg 31:31

What

Vanessa Vakharia 31:31

as a cliffhanger. We play, we play that clip right now and then say, do you guys want a part two where we talk about this clip?

David Kochberg 31:39

But since we've got everything set up, we should just do part two. After you

Vanessa Vakharia 31:43

call, I have a phone call, but here's the thing. I have a phone call with Jamie Mitchell and I actually think we should call him because he is. An amazing math educator who loves ai. His whole thing is ai. Well, let's not, let's call him live.

David Kochberg 31:56

No, no, no. That's gonna be a sonic mess, but just get him on the podcast down the road.

Vanessa Vakharia 32:01

Okay, fine. Um, okay, so I think. But how am I gonna play the clip? Oh, you're gonna just insert the clip?

David Kochberg 32:07

Well, we don't have to play the clip. We can just, oh, you wanna play the clip?

Vanessa Vakharia 32:09

I think we should play the clip. Okay. So hold on. We're well here.

David Kochberg 32:11

Pull it up.

Vanessa Vakharia 32:12

We have to end this episode. We have to end the episode. But I hope we talked about something

David Kochberg 32:16

I, well, we talked about, we must have, we've been talking a lot, so.

Vanessa Vakharia 32:23

I think the focus of this episode, to be honest, was a little more on tools and like when do tools help and hinder? Because even what you're saying at the end there about being like, well, we're all problem solving in our own ways. Like if you've memorized formulas and you're trying to figure out what formulas to use when that is mathematical thinking, you're problem solving. And I do feel like when I'm writing a song, I'm drawing on all these things. First I do a thing, maybe I have a top line. So I'm top lining something. I've made all those lyrics myself. Maybe then I get stuck on a chorus. So then I ask you to help me. So now you've helped me. That's not my own thinking, but that spurs something in me. Then you say something and I need to rhyme. So then I look at the rhyming dictionary. Yeah. That's another tool that I'm using. Yeah. Then I get stuck on something. So I listen to a bunch of songs I already know to see, like to get some melodies in my head that I got inspired by that. So then I write something else and it's like in all of these, none of these are pure. Thought free from influence.

David Kochberg 33:14

Absolutely. And it is a question of to what extent should we be reliant on tools versus whe at, at what point are we the tool? Oh, do you mean like, I mean, I, I said that 'cause I knew it would sound cool, but it doesn't mean anything, but No, no, no, no, no. I think it's good. No, I think at, at what point are we overly relying on tools to the, to our own detriment versus, versus how. Can we make sure to be responsibly using all of these tools while still to move us forward instead of hold us? Yeah. While still accomplishing, being productive and growing as people because that's what I do Worry. About like society in general. Yes. But then also for education, especially students, because students are growing up in this world. They're so screwed.

Vanessa Vakharia 34:07

I feel so bad for them.

David Kochberg 34:08

Like we know a time where we only could rely on our Yeah. Uh, like we, there was no option. I mean, you could get someone to write an essay for you, or you could like copy someone else's test, but you can't Yeah. The idea that any stu no, no teacher can know how, uh, okay. We, we have to stop. We have to stop. We have to stop. Stop. This is how every, we're stopping

Vanessa Vakharia 34:26

this. We started by saying, is math no? By claiming mathematical thinking. Is the same as pop sensibility. I have three points. The first was the role of tools in songwriting. This idea of friction, maxing, productive struggle. When do tools hinder more than help? Because that you, when you ask any songwriter, they have a whole bunch, everything we're talking about right now they use and they use one another. They collaborate. I want you guys as we, the point is I had two other points, which was the rule of creativity and. Point number three was the rule of math and what we think math is in both of these things. We are gonna save those. Sure. I'm, I'm, here's what I want you guys to do. I've got some homework for you. Number one, I want you to go to one of your favorite songs. I want you to look it up on Spotify. If you use Spotify, sorry to promote them. You can use any platform. I just know how it works in Spotify, where you can find the song credit. Okay. And I want you to go to the song credits for any of your favorite songs, and I want you to go look at how many people created that song. Go to the songwriters and see. You are gonna find that almost any song out there that you're like, oh man, so and so wrote this. They didn't write it, they wrote it along with a team of people using that as a tool. Collaboration is a tool. Other people are tools. So I want you to go look at that right now 'cause I think you're gonna be shocked. Because again, we don't have time to talk about this now, but collaboration a thing that we are now trying to promote in math class because so many other countries and societies use collaboration as a tool. We've looked at it as a solo sport in songwriting, the same thing. You get a better product when more minds work at it, but that is a tool. So I want you to go look at that. Second thing I want you to do, I told you guys to look up our band. Goodnight Sunrise. I want you to look up.

David Kochberg 36:08

How many songwriters? There were songs? No, no.

Vanessa Vakharia 36:10

I want you to go look up the Velvet Sundown.

David Kochberg 36:12

Oh,

Vanessa Vakharia 36:13

okay. Do not confuse the two. Velvet Sundown is an AI band. I want you guys to go listen to them and check them out and tell me if you can tell that they are not real because I could not tell. Then go listen to our band. Goodnight Sunrise. Okay, number three, text us and tell us if you want. To hear the rest of how mathematical thinking is like pop sensibility. 'cause I do have a lot more to say. I do worry that this is a bit in the weeds, but we're here now.

David Kochberg 36:41

We're really gonna rely on texts to tell us if we could do this or not.

Vanessa Vakharia 36:45

Yeah, I think we just record the other. We gotta really

David Kochberg 36:47

pick our callouts.

Vanessa Vakharia 36:49

Well, I think we need to know.

David Kochberg 36:51

Fine,

Vanessa Vakharia 36:51

just send us a text. You can find the number in the show notes of whatever podcast. Listen,

David Kochberg 36:56

let's know if this was any good and if I should not be on episodes. No.

Vanessa Vakharia 37:01

Okay. Um. And tell us what your favorite song is.

David Kochberg 37:05

Did you wanna, do you wanna play your, you tell us. Tell us what your favorite song. Do this? Yeah. Pick your, tell us what your favorite song is and look up who are the songwriters and what the songwriting splits in the publishing. No, don't let that

Vanessa Vakharia 37:17

up. But honestly, look up, tell us what your favorite song song is. Let us know what

David Kochberg 37:20

key the song is. Tell us what your favorite song is. What and what

Vanessa Vakharia 37:23

and how many songwriters there were

David Kochberg 37:24

on it. Is there a congratulations? 'cause this

Vanessa Vakharia 37:26

will actually help for the next episode if people want, when we can dissect some of these songs. And talk about the pop sensibility and how it's like math. We have to go. It's your podcast. Fuck. Okay. Bye. Thanks for listening, guys.

Why do so many artists have math trauma?

Vanessa Vakharia 37:40

Thanks for listening. Yeah, bye bye. Oh my God, chaos. That was actually chaotic. Let me call Jamie because honestly like I'm so late to call him. Let's just see if he wants to say anything. Oh, no. We were supposed to play that clip as the cliffhanger.

David Kochberg 37:58

Fine. Okay. Now we're gonna play the clip of the cliffhanger that we didn't actually reference or talk about in the show at all. However, it's, this is the reason we, Vanessa even wanted to talk about it. 'cause I listened to this episode and I thought it was great and I told her to listen to it 'cause it would help her and it took her five days and she finally did

Vanessa Vakharia 38:15

Explain who Amy Allen

David Kochberg 38:17

is. Amy Allen is a. A highly accomplished songwriter who's co-written songs for Tap Harry Cry. Harry, Harry Styles, uh, all sorts of, uh, yeah, I mean, those are two the biggest hit me, uh, Sabrina Carpenter. And so, yes, she was on this, she was on a podcast called Switch on Pop, which I'm a big fan of. Here we go, and here we go. Okay. Wow. But then you're gonna

Vanessa Vakharia 38:37

just listen to this clip.

Switched On Pop podcast 38:39

How many songs were you writing that year?

Amy Allen 38:42

I am really bad at math. That's why I got into songwriting. But I don't know, like, so too many

Vanessa Vakharia 38:47

okay. And there's another clip. Another clip. One more. Okay. Uh, the

David Kochberg 38:51

chuckles. The chuckles in the audience. Yeah. Everyone the knowing chuckles. Ha ha. We all hate math too. Here we go.

Amy Allen 38:59

No pre-course.

Switched On Pop podcast 39:00

No pre-course,

Amy Allen 39:01

right to the chase. I

Switched On Pop podcast 39:02

mean on, on one level. It's very simple. Mm-hmm. Just sort of rolling. Eighth notes.

Amy Allen 39:07

Mm-hmm.

Switched On Pop podcast 39:08

Simple pentatonic, melody.

Amy Allen 39:09

Oh no, we're getting into math.

Switched On Pop podcast 39:10

Oh, sorry.

Amy Allen 39:13

I'm kidding.

Switched On Pop podcast 39:13

But the phrasing, hear everyone

David Kochberg 39:15

laughing. Sounds like Amy Ellen has math trauma.

Vanessa Vakharia 39:18

I think we should get it on the pod.

David Kochberg 39:19

Get on the pod. We have to end this episode. Goodbye, Vanessa

Vanessa Vakharia 39:22

Text us. Love you. Bye. Okay,

Jamie Mitchell unkowningly calls in

Vanessa Vakharia 39:25

lemme call Jamie. Should I record you and Jamie talking? Let's just see what he says. Let's just like quickly see if this works. I'm late, Jamie. Hey girl. You're on the podcast. We're gonna try and just put you, you're on the mic. I'm so sorry to do this. No, I'm just so close to the mic.

Jamie Mitchell 39:41

Gimme this. I didn't agree to a podcast.

Vanessa Vakharia 39:44

I know. And you're not gonna really be on it, but we're just gonna record this in case it works because the reason I was late is. We just did a whole episode that really went off the rails. It was supposed to be about how, 'cause we're rewriting our album. It was gonna be about how pop sensibility is the same as mathematical thinking. But we've been talking a lot about how AI music, like even though the outcome of an AI generated song is a great song. It. We don't like it. And I then I had this call with you and then, sorry, this I'm really not explaining. Well, David is shaking his head at me. But then, then I was like, this is, I was like, this is exactly like math. Like it's like even if the outcome is the right answer, if you just asked AI to get it, like we wouldn't like it. And then I was like, oh my God, I'm late for my call with Jamie. We should just get his opinion. 'Cause he loves AI so much.

Jamie Mitchell 40:33

I do. Do you want my opinion now?

Vanessa Vakharia 40:37

Kind of like, like, like just a brief, like I,

David Kochberg 40:40

I cautioned against this, just so you know. I didn't think that suddenly putting you on the spot on a phone call was the best way to discuss on a podcast, but hey, it's.

Jamie Mitchell 40:51

Sorry, this is David.

David Kochberg 40:52

Yes. Hello. See, I'm, she's like, does he even know? I don't even know. Who is this? Who, where, where are we? What is happening? Hello, I'm David.

Jamie Mitchell 41:01

Um, I, I, I'm Jamie. Um, I do enjoy being put on the spot for spicy Hot Takes.

David Kochberg 41:06

See. All right. Well, yeah. Well, we're, we're recording. You

Jamie Mitchell 41:10

didn't, you didn't know that about me. Um, so, okay. What do I think about AI generated music and AI generated math?

Vanessa Vakharia 41:21

Yeah, like, idea is that the outcome is the same, like a great song is a great song. Why? Yeah, I

Jamie Mitchell 41:29

think it depends on like what, what the intent of the person who's asking the content to be created is, right? Like I could be great at writing lyrics and I might not have anyone who could write music for me. So if I write a beautiful set of lyrics and then I ask AI to set it to music. I, I personally don't fundamentally think that's a bad thing. That is like a proof of concept to me. Um

Vanessa Vakharia 41:58

huh.

Jamie Mitchell 42:00

Do you know what I mean?

Vanessa Vakharia 42:01

Wow. Keep going.

Jamie Mitchell 42:03

Okay. So I think it's the same, it would be the same for me for math if I. I don't know. Let's say I'm trying to make a simulation for a game to collect some data to, to do like a, a project, but I don't know how to code up this in computer code or in a spreadsheet, but I, I'm, I'm still interested in it. I'm still engaged in it. If I can tell the AI what I wanted to do and know enough to evaluate if it did it properly. I don't think there's anything wrong with that, especially if I'm using that to go deeper with math. Flip side of that, if I'm. Uh, AI write me a song and I don't do give any thought to it. I don't put any of my own creativity or my spark into it, and it just pumps out this soulless piece of music. Like those, I think those are two different things.

Vanessa Vakharia 42:52

Hmm. So I guess the question is who's right? Like, do we have different thresholds? Because like, I don't know, David, I don't think, do you agree with him with that song thing? Because you guys are the polar opposite. Like David hates ai, like he hates when I even use like a rhyming dictionary. Like he's like very concerned about ai.

David Kochberg 43:14

well, there, there's lots of different layers with, with like with songwriting. So the idea that you. If you wrote all of the words, all the lyrics, then yes, for sure that's an original creation from you. But then putting that, just putting those lyrics then as just text prompt into a song creator. If you don't have musical ability, then it would be better for you to collaborate with other humans who do have those complimentary skills and then make an original piece of music that way, as opposed to just having. A program or an algorithm, do all, all of the other stuff yourself for you. I'm not explaining very well, but

Jamie Mitchell 44:00

No, no, no, no. I, I totally understand what you're saying and I don't, I don't think I disagree with you. I think the more like, I think humans are important, especially when it comes to. Creative arts. Right. And I think math is a creative art. Um, but I, you know, when I think about the students that I work with, they don't necessarily have access to people that can play an instrument, but they might be very creative with. Their lyrics. And for, for some kids that would be the end of the road, right? Like, you know, they're, they're self-conscious. They don't wanna put themselves out there. They will, they write these things and they go nowhere. Um, or if, if they can, they can, they can at least make something musical to help them see their vision, which gives them a, like a stepping stone.

David Kochberg 44:44

Mm-hmm. Well, I guess the other thing is then is what

Vanessa Vakharia 44:47

about people who write with beats? Yeah. Or like loops, like all the

David Kochberg 44:50

Yes. Yep, yep, yep. Yeah. Yeah. Yes. And that's why I'm not, I'm not like a puritan about it. It, it is a preference for me and I do think I am also often speaking philosophically and thinking of a worse case scenario in terms of like, do, is humanity gonna over time rob itself of our inherent creativity if we keep sort of outsourcing it? Because then another. Like a devil's advocate thing could be so and totally fair about access to things and like, privilege can enter into it. 'cause Yes. What if someone cannot afford a guitar? Mm-hmm. But if I'm, if, if like someone can get their hands on a guitar, let's assume even a piece of crap guitar then if you. Can come up with some ideas for a song or some lyrics or melody, and then just shortcut by saying, Hey, write me a guitar based song with these lyrics. And then you're like, okay, I wrote a song. If this is something that's important to you and you're passionate about, would you then be like, well, I guess I should like learn how to play guitar, and then maybe learning how to play guitar over the course of years would be something that you've developed and feel proud of and allows you to, to express yourself. Like that's, I guess, what my kind of concern is, like all things being equal, lets say it if, if we become too reliant on these easy shortcuts to get to something. Then does it rob us of abilities to discover new things about ourselves?

Jamie Mitchell 46:25

Mm-hmm. This has been my work for the past y you know, year and a half is working with teachers to get them over the, like the fear of ai, right? Like, it's not going anywhere. It's a reality we have to deal with. So what can we do to convince students of the exact thing you're saying, right? Like

Vanessa Vakharia 46:44

Yeah, it's,

Jamie Mitchell 46:44

it's a tool that can suck all the soul out of everything we do. If it's used poorly, in it's worst case, that's what's gonna happen. But you know, there, there are also examples of students who've used it as a brainstorming partner, like a thinking buddy, and have enriched their own understanding of material. Just, just by having that extra outlet. Mm.

Vanessa Vakharia 47:07

Okay. So I think we should just have, do a full episode on this at some point with you. Obviously.

Jamie Mitchell 47:11

I'm game.

Vanessa Vakharia 47:12

Okay, great. I guess we should end this. Yeah, we should have,

Jamie Mitchell 47:15

it's not like a job interview.

David Kochberg 47:17

Yeah. Like you, you passed the test. Okay.

Vanessa Vakharia 47:21

You can be on the podcast.

David Kochberg 47:22

Okay. Okay.

Vanessa Vakharia 47:23

We're ending this episode, but is this

David Kochberg 47:25

conversation actually going on the

Vanessa Vakharia 47:26

podcast? Sure. Yeah. Okay. Bye. Ja. See, look, I'll say bye to Jamie.

David Kochberg 47:29

Okay, great.

Vanessa Vakharia 47:30

Bye. But don't hang up. Bye bye, Jamie.

David Kochberg 47:32

Bye Jamie. Bye Vanessa. Bye. This is just like every other episode ending.

Vanessa Vakharia 47:36

Okay. Okay. Now over to me and Jamie. So sorry about that.