Math, Music and Mayhem

It's not you know, it's kind of like a ven diagram I would imagined. But um, see there you go with the math. Yeah goodness, yeah, goodness me because this is exactly what we're talking about. Math and music, um, kind of lining up with each other, um, describing each other. And we end up with this this idea in our head, especially uh, those of us who are not math people and enjoy music but don't have musical training per se um.

We end up looking back at it where we see mathematicians who are really good at music or musicians that have mathematical background, and we start saying, WHOA, what's going on here? This seems to be the case, right right, And I think you made the great analogy yesterday, like, oh, actors, yeah crazy, all actors are crazy. Right. It's like if you if you don't have an acting background, you don't know many actors, you're not crazy. You don't know many

crazy people. You see crazy actors, and it's easy to make that generality that, wow, they must be All actors must be crazy, and their craziness must make them great actors. Or maybe their acting makes them great crazies. I don't know. Yeah, yeah, it's the that's the dog wagon the tail there. Um. So yeah, we're going to try to look at this idea of math and music being intertwined in perhaps being inherent and um, and we'll try to see if there

really is a correlation between mathematics and musicians. Yeah. Now, just to start off, like some famous mathematicians and slash musicians or famous musicianstead have mathematical background. Um. One one hand, we have Einstein himself, who was a violinist. Yeah. Um, Brian May of Queen was an astrophysicist, um, which I've always found kind of interesting. I don't know if it really I haven't listened to queen in a long time, but I don't remember there being much astrophysics UM injected

into the song. Yeah, maybe it was all happening just with the music, just with the guitars, you know, because and he he has returned to this discipline. Yes, yeah, yeah, yes, yeah, there have been some interesting articles about it in recent years. UM. Then we have people like Dan Snaith a k a Caribou who has a mathematics background, though I've seen interviews where he's very dismissive of the idea that there's any really connectivity between the two. I think it was like

a was it an interview on data transmission? I can't remember me it was linked to on data transmission UM that code out UK where someone asked him about in Cariboo was like you know math, yeah, math, math, different things. So it's kind of disappointing. You can imagine the the interviewers, you know, kind of slumping down, you know when he got that answer. But other ones are Garfuncle had a master's degree in mathematics, which I was not aware of.

I wasn't. I was surprised by that one. Yeah, I mean, certainly his hair seems to indicate some sort of like science lab type situation. But but no, he and again I can't think of any Garfuncle songs where where I have listened to him and be like, wow, bright Eyes is such a mathematical song, you know. And again maybe I'm I'm missing the finer corners of his discography, but yeah, um. And then another one that comes to mind, uh is a chat by the name of Rupert Way, who DJ

is under the name dj Irk. Yeah, and I actually interviewed him for the blogs a little while back, and uh, he has like a PhD in uh, some kind of type of mathematics that dynamic systems something. It kind of it just goes right over my head when when he told me what it was. But but yeah, And there're just a few there. Do you have any that I'm leaving off? No, No, that that sounds Um, those are some of the big ones, I think. And I was I was actually revisiting your interview with him, and he

was talking. You were asking him about the connection between Mathew music and I think he was saying that he doesn't it doesn't really help anymore than it does with what he says, say around trip a trip around the supermarket. I've obviously taken that out of context. Uh, but he did say something about mental agility, good memory, good numerous e and a lot of determination, he says, or what really counts. And although these are math related I'm quoting him,

they are not math specific. There are lots of overriding instinctive and emotional factors too, which I thought was interesting because he's he's sort of saying, yeah, all of this helps, but it does not make you a musician per se, because there are some factors that you just can't that don't fit into the mathematical model, so to speak. Right. Yeah, his answer was far more insightful than caribous. Yeah, yeah, yeah,

he actually he went on to say some very interesting stuff. Actually, So if you haven't checked out Robert's blog on that with with dj Oric, should definitely check that out. Yeah yeah,

I'll throw the link up. But but yeah, you end up in the in this this situation where the the answer is kind of yeah, kind of yeah, but also not really um and and there's no real firm answer because I mean, when you break it down, UM, I mean we we've discussed in the past, like mathematics, what is it is the human invention that just is so clever that it describes everything in the universe? Or is it a discovery? Did we find the secret language of

the universe and we're so awesome because we found it? Again, humans end up looking pretty awesome. Either way, you spend that but if but but but either way, you're talking

about a system of numbers that can describe everything. So it stands to reason that it would be able to describe music, right, Right, And yes, so there are definitely some similarities with that because you would ask the same thing about music in a sense, right, it is music something that we discovered is just sort of inherent in

in us. And then we've talked about even our fingers before, Right, we've got five fingers on each hand, and how that's determined our currency in the way that we count in number systems, and same thing with music. It's it's determined the way that we have, Uh, created scales, and we created instruments. Yeah, like strings vibrated a certain frequency and you can measure those mathematically. Sound waves can also be

described by mathematical equations. Uh. I mean it comes down to like scientists of any discipline, they use mathematics to describe the physical world. Changing physical world of movable opjects, and they predict the outcome of physical process, so you

know there's gonna be some cross over there. But then again, an equation is not going to be able to describ have a piece of music, and uh, I mean there are a certain mathematical well, well you can there are equations that can describe some of the mathematical structures that are inherent in music, but you're not going to be able to like to say, um, yeah, I want to listen to that. Um, you know that can concerto by so and so, But I don't have time for the

full thing. Just send me the equation. Well, and it's interesting too, because the each equation you could interpret in a different way as a musician, right yeah. But I mean so there's that's the part of it that's like, well, okay, here's here's the precise language. Um that you know, and again drawing parallels to math, Math has a universal precise language. Right.

But once you know, you give this equation of music to someone, they might perform it in a completely different way or take liberties with it that you wouldn't necessarily see in math. But again again talking about similarities, Um, both disciplines gravitate towards symmetry. Right. You see this in music all the time. Um, of course there's there's cacophony, right, Uh yeah, noise music and all that. I mean that's the thing too. It's like music when you're talking about

like what is music? Yeah, there's some there are there certain types of music that are very mathematical sounding, and you can break down you can you know, apply some some number to the numbers to the music theory of it all, and it makes perfect sense. But then you pull out some sort of like noise artist where they're using very abstract sounds music that uh, to quote my wife,

sounds like someone through a xylophone down a stairwell. And then it's gonna be hard to say like, oh, well, mathematically, this is what's going on there. But then again, you could also make the counter argument that even a chaotic system, um, there's math going on there. Can you can go back and forth. And now the ancient Greeks they definitely thought there was there were numbers tied up in music, that

math and music were very closely related. Is this uh pithe Pythi versus yeah, yeah, yeah, like because he use all about the ratio of yeah, yeah, and his his whole like system of of education. Um. They considered music to be a strictly mathematical disciple in involving number of relationships, ratios and proportions, and so if you break it down, it would basically be a subdivision to quantitative mathematics in

Pithagorean time. So yeah, harmonica ratios proportions central in the Greek's understanding too musical, okay, yeah, And so just to back up a little bit to the five tone or the pentatonic scale developed about three thousand years ago in China, and then the Greeks they have the seven tone scale, right, um. And then then we're talking about the twelve tone scale, right, And this is when we're talking about Pythagora is really

obsessing on these ratios. And I won't go into the math behind it, but that's how we sort of came up with these varying skills. And it wasn't till around I think Box time where they took one of those ratios that was a bit off and and tinkered with it and they came up with the final twelve tones. Um. So again there's there's a system behind there. There's math that's driving the way that we are expressing music, which is pretty interesting, all right, But what exactly is going

on in the brain? Right? Yes? Yes, so let's uh, let's take a quick break, and when we come back, we will look at math and music in the human mind. This presentation is brought to you by Intel sponsors of tomorrow,

and we're back music brains. What's happened? Yes, um, so, obviously scientists have looked at the brain and analyze what exactly is going on when we think about music or contemplate music versus contemplating math, and they have Scientists actually looked at brain injuries that suggest a single region in the left hemisphere of the brain gives rise to sequential analytic processing, which is used for both doing algebra and

reading music. All right, But then on the other hand, there was a two thousand eight study from the University of Arkansas that used a human Information Processing Survey instrument or a HIPS instrument to measure hemispheric collaterality. They used a hundred and one participants asked them to discuss their prowess in first math and then in music, and their finding suggested that math is a left hemisphere preference and

music is a right hemisphere preference. Okay, well, it's interesting, right because we've talked about music before and how it affects the brain, and we've found that there is no one music center, um, so it's sort of spread up throughout the brain. But to to know that's obviously engaging in a part of the brain that is that's tracking um math is interesting. And likewise, there have been a number of studies which sort of say different things about

exactly how musical education affects one's mathematical prowess. Um. They have been studies they've found that people with musical training outperform people who don't have musical training. Um. But then there's uh, there's stuff like for instance, there was the Montreal Montreal Piano Project. All right, half the children were giving piano lessons for three years, and after two years, the piano playing kids were outscoring the others on spatial ability.

So the argument here was that yeah, learning music helps you, um helps you with math because it's reinforcing the brain circuits that power spatial thinking, which comes in handy not only for knowing what keys match up with what note, but also in geometry, physics, and chemistry, all right, But then opposing that we have um um a study from the University of Toronto. Uh, and this one, this one

was pretty cool too. They took six year olds, all right, and they took weekly piano and singing lessons throughout the school year, and they exhibited an average i Q increase of seven h point zero points. Right. The other six year olds who took either weekly drama lessons or received no extra trick curricular lessons displayed an average i Q rise of four point three points. So that's another one that also seems to indicate, all right, they're they're learning

music and this is helping them with their scores. But I also think, like non scientifically, that maybe the drama kids were just having more fun and didn't have as much time to really play with the studying all that much. Huh, all right, yeah, they were too busy emoting. And then the kids who didn't get anything, they were just setting around in study hall like destroying desks with tiny axes

or something. They weren't having new experiences. And we just talked about this so important is that you need to to have new experiences in order to create new pathways. Yeah, discussed in our Einstein's Brain podcasts. Alright, so there's there's some basis here for some some waltzing, let's say, between

between the brain and music and maths. What I was interested in knowing was whether anybody had ever actually taken a piece of music and said, okay, here's here's here's some math right here, right, because there are certain pieces of music that I hear sometimes and I'm like, god,

I can I can't. Maybe geometrically, I can see things going on in this music, um, which is sort of interesting way you're talking about in your mind, not the not the visualizer that pops up, yeah, exactly, not in front of my computer with you know, I don't have like purple splashes. Um. But what I found was that

there is a book called meta Magical Femus. It's called Questing for the Essence of Mind and Pattern by Douglas host Daughter And he actually looked at Chopin's music and box as well, but he said, Chapon's music is filled to the brim that I'm quoting with algebra algebraic tricks of cross rhythm. A famous example is in his iconoclastic waltz Opus forty two in a flat major written eighteen forty and this waltz. The baseline follows the usual oompapa

convention of the waltz. I don't know if papa, yeah nice, yeah, okay, okay, But the melody of the first section completely counters this three nuts. It's six six eighth notes. Instead of being broken up into three pairs aligned with the left hand bounces while playing form two triplets. The initial notes of the success of triplets are to be clearly emphasized and prolonged, thus creating a higher level melody abstracted out of the quietly rippling right hand. Yeah. I think I'm gonna have

to hear an example and put that together. Yes, yes, And he's saying that this melody is composed of two notes per measure beating regularly against three notes of a waltzing base. And he says it's a marvelous trump let aier effect, which which means the oral equivalent to an optical illusion. Basically, So let's take a quick listen to uh this waltz. It was forty two in a flat major. I don't know, did you hear it? Um? Yeah, I think I can. I can get a sense of some

of that coming together. I definitely got the oom Papa. Yes. So that's one example where someone has actually tried to map this, which is kind of interesting. And um. There was another example that I found by mathematician Hence Strob, and he talks about modal jazz. And the reason I really wanted to look into this is because jazz modal jazz is uh is someone like uh, it was like Miles Davis. Miles Davis is usually attributed to be the person that that sort of creative medal jazz are popularized

it um, particularly in the fifties. So this modal jazz is is said to have a more horizontal structure, whereas traditional jazz is structured more vertically, and modal just means that he took a bunch of notes and he sort of squished them all in this my my horrible understanding of both mathematics and UM and music theory. Um. So it just seems weird that jazz would like I thought jazz was free flowing, man. I thought you can't put math on jazz. Jazz as its own rhythm. Yeah, well

that's the incredible thing. And that's why I love Miles Davis is because it does seem like there's a lot of um sort of off off the cuff playing, right, But I mean, the fact of the matter is is that they're taking some some very um concentric like rhythms

and then they're playing off of that. So what you might hear which sounds sort of like, oh wow, man, that that cat is just going nuts on the saxophone, Um, they are, but but they're doing it in the sort of loops, um, these horizontal loops, and they're not doing a lot of key changes. So let me try tokay. So, like, if you had like a really crazy story that that that at its heart followed a traditional story arc, even if it involved like art arts from Mars in love

with each other or something. Yeah, yeah, And everybody knows that that once you start, you know, to be good at any craft, right, you have to know the absolute basics. You have to master it. And um, you know, Myles Savis is someone who certainly was master at what he did, So that gave him the othery to sort of riff off of stuff and um, play with modal notes and and do all these sort of different things that actually

changed people's perception of that music itself. So what I thought was interesting about it is that this this guy Hendstrub, he talks about the traditional jazz being structured more vertically, which means in this context that traditional jazz impro improvisations are based on chord progressions and modal jazz. On the other hand, improvised improvisations typically go on for long periods

without any chord change. So that so I was talking about earlier, and the interest is more turned towards the melodic line. Uh So, it's it's a That's why I thought it was sort of interesting to me because I thought I can see that visually. I can see that in Miles Davis's music. You can see this horizontal spreading. You can see in Yo yo mom when he does uh the box suitets um. You can see it maybe

even in like PJ. Harvey and like White Chalk, like the Cults an album that has sort of like this horizontal spreading, although you could say there are some there's some vertical loops of coophany in that as well. But anyway, let's let's just listen to a quick clip from kind of Blue Miles Davis. Cool. Yeah, Now, did you say this is actually your favorite track, your favorite song, favorite album? I mean the entire album is my favorite. There's actually not one song on there that I would say that

is my absolute favorite. I love it as a whole piece, and um, you know we've talked about this before and getting in the zone, and um, this is one of those pieces of music that I can listen to and it does sound it kind of put me into a different state that allows me to think clearer, think at higher levels. I think, is why I like it. And also we've talked about this too, like lyrics sometimes bother

me when I'm trying to cogitate up in Monogaen. So you know, that's that's that's some of the discovery here where we're seeing that the music and the math, at least again geometrically, I can see it. I don't know if it's the same for other people. But there's a guy named Dave Russ, and he's associate professor of mathematics at Northern Illinois University, and he really does try to make this correlation between music and math, and he thinks

it's important for for students to better understand math. In fact, well, he says mathematics, like music, embodies certain patterns and ideas which don't translate well into words, as we found out. Uh, as you listener, hath end up. We can feel them, see them, understand them, but only after we have really worked to lift them off the paper and into our minds, only after we've tried to see where they come from, only after considerable practice with the minutia, gradually adding the trills. Uh,

do we have the full spirit of the idea? Mathematics like music as a human adventure, people create and discover it, they try to then share it and enjoy it. Yeah. I mean I I definitely found that to be the case with both music and mathematics, because on one hand, I love um certain genres of music, and I'll you know, I'll listen to it all the time, but I'm not

necessarily really good at describing what's great about it. Like if if I'm like, you know, talking to a friend, I'm like, oh, you gotta listen to this new mix by so and so, and they might be like, well, what's awesome about it? And I may be a little stump for words, you know, unless I have some time to prep. Likewise, with mathematics, I was the last week I was working on an article about number theory and

like number theory. Especially when writing for a general audience and a you know, non math audience, it's it quickly becomes a conversation that cannot be really held in English but needs to be held or any language, but needs to be held in math. You know, it needs to be held with numerals and and equations. So it becomes increasingly difficult to to explain the topic without being the

topic right right. And that's why us wildly humans, I suppose, turned to math and music to try to express ourselves and our ideas and in a better way. Yeah, because I think I saw it pointed out that both both music and math are like they're self describing things. The music describes itself, the math describes itself, and h and yeah, at the at the end of the day, it kind of sounds like, you know, defeatist, but they both kind of described themselves the best. There we go looking in

the mirror. I'm trying to change the world. I don't know I was trying to do, Michael Jackson, there apologize you were trying to do like an impersonation. I was thinking that math and music we're looking at each other in the world. And then excuse me, looking at each other in the mirror, and then I started thinking about that song man in the mirror. Oh, it's just bad all around. No, No, it wasn't that bad. It was good.

You did fun um. If we have the speaking of math, we have a listener mail here, a listener by the name of Timothy. He says, hello, stuff to all your mind crew. I just wanted to say thank you for the unusually deep mathematics podcast. I am a science and philosophy enthusiast, and I just happened to be in the middle of a book called A World Without Time, the Forgotten Legacy of Godal and Einstein when you aired your podcast.

I personally believe that Godal's incompleteness, theorems, the existence of non eucludean geometries, the necessity of imaginary numbers, and such all point to math is a formal system invented by humans. It strikes me as something similar to a game like chess, where simple rules give rise to an incredibly complex overall system. I could imagine a chess like game being created to model physics. What is interesting to me is that Godal,

like many mathematicians, was of the opposite persuasion. He believed that math exists independent of the human mind. By the way, one of my favorite books is also godal escher Bach by Douglas hofstadtur Hofstadter Yeah, can we as ye, which I highly recommend it to any listeners who also enjoyed the Math podcast. Thank you for all the hard work you to do, Tim. Thanks Tim. Yeah, so, yeah, the we have the podcast that we've in referenced earlier. Um

is math a human invention or a human discovery? And uh, yeah, that was a lot of fun to do. Yeah it was. And and uh again, we were both a little bit trepidacious about, you know, entering into the realm of math, but it turns out it was not painful at all. Yeah, And if you want to enter into our realm, then all you have to do is check out Facebook and Twitter. It is not painful either, not painful at all. I mean unless like twitters down or something, and it can

be a little frustrating. But now we'll blow the mind on both of those and we update that with all sorts of links to cool stuff. We're reading cool stuff, we're writing cool stuff that we just podcasts about, and we would love to hear from you. So Please feel free to drop us a line at blow the Mind at how stuff works dot com. Be sure to check out our new video podcast, Stuff from the Future. Join how Stuff Work staff as we explore the most promising and perplexing possibilities of tomorrow.