WEBVTT - Math, Music and Mayhem 0:00:03.800 --> 0:00:06.680 Welcome to Stuff to Blow your Mind from how Stuff 0:00:06.680 --> 0:00:13.920 Works dot com. Hey, welcome to Stuff to Blow your Mind. 0:00:13.960 --> 0:00:17.000 My name is Robert Lamb, and I'm Julie Douglas. And 0:00:17.400 --> 0:00:20.880 you know, Julie, neither of us are really math people. 0:00:21.680 --> 0:00:24.280 It's like we don't do a lot of recreational math. Yeah, 0:00:24.360 --> 0:00:26.200 and we know. I'm a math folk. I just started 0:00:26.200 --> 0:00:29.120 to same math and I started to get sweaty palms. Yeah. 0:00:30.400 --> 0:00:33.080 Um and uh, but but but but we both enjoy music, 0:00:33.120 --> 0:00:35.760 different types of music, I think. I mean there's some crossover. 0:00:35.840 --> 0:00:38.040 It's not you know, it's kind of like a ven 0:00:38.560 --> 0:00:41.640 diagram I would imagined. But um, see there you go 0:00:42.080 --> 0:00:45.360 with the math. Yeah goodness, yeah, goodness me because this 0:00:45.440 --> 0:00:49.360 is exactly what we're talking about. Math and music, um, 0:00:49.479 --> 0:00:52.640 kind of lining up with each other, um, describing each other. 0:00:52.880 --> 0:00:55.840 And we end up with this this idea in our head, 0:00:56.000 --> 0:00:59.520 especially uh, those of us who are not math people 0:00:59.840 --> 0:01:04.960 and enjoy music but don't have musical training per se um. 0:01:05.040 --> 0:01:07.360 We end up looking back at it where we see 0:01:07.920 --> 0:01:10.520 mathematicians who are really good at music or musicians that 0:01:10.600 --> 0:01:13.280 have mathematical background, and we start saying, WHOA, what's going 0:01:13.319 --> 0:01:15.520 on here? This seems to be the case, right right, 0:01:15.720 --> 0:01:20.039 And I think you made the great analogy yesterday, like, oh, actors, 0:01:20.360 --> 0:01:23.960 yeah crazy, all actors are crazy. Right. It's like if 0:01:24.000 --> 0:01:25.920 you if you don't have an acting background, you don't 0:01:25.920 --> 0:01:27.959 know many actors, you're not crazy. You don't know many 0:01:27.959 --> 0:01:30.160 crazy people. You see crazy actors, and it's easy to 0:01:30.160 --> 0:01:33.639 make that generality that, wow, they must be All actors 0:01:33.720 --> 0:01:36.240 must be crazy, and their craziness must make them great actors. 0:01:36.400 --> 0:01:39.480 Or maybe their acting makes them great crazies. I don't know. Yeah, yeah, 0:01:39.520 --> 0:01:42.320 it's the that's the dog wagon the tail there. Um. 0:01:42.360 --> 0:01:43.840 So yeah, we're going to try to look at this 0:01:44.200 --> 0:01:49.080 idea of math and music being intertwined in perhaps being 0:01:49.160 --> 0:01:53.280 inherent and um, and we'll try to see if there 0:01:53.280 --> 0:01:56.720 really is a correlation between mathematics and musicians. Yeah. Now, 0:01:56.960 --> 0:02:00.680 just to start off, like some famous mathematicians and slash 0:02:00.800 --> 0:02:04.720 musicians or famous musicianstead have mathematical background. Um. One one hand, 0:02:04.760 --> 0:02:09.919 we have Einstein himself, who was a violinist. Yeah. Um, 0:02:10.000 --> 0:02:13.880 Brian May of Queen was an astrophysicist, um, which I've 0:02:13.880 --> 0:02:16.280 always found kind of interesting. I don't know if it 0:02:16.360 --> 0:02:18.720 really I haven't listened to queen in a long time, 0:02:18.720 --> 0:02:22.400 but I don't remember there being much astrophysics UM injected 0:02:22.440 --> 0:02:26.960 into the song. Yeah, maybe it was all happening just 0:02:26.960 --> 0:02:29.400 with the music, just with the guitars, you know, because 0:02:30.080 --> 0:02:33.760 and he he has returned to this discipline. Yes, yeah, yeah, yes, yeah, 0:02:34.000 --> 0:02:37.120 there have been some interesting articles about it in recent years. UM. 0:02:37.280 --> 0:02:41.080 Then we have people like Dan Snaith a k a 0:02:41.200 --> 0:02:45.520 Caribou who has a mathematics background, though I've seen interviews 0:02:45.520 --> 0:02:48.160 where he's very dismissive of the idea that there's any 0:02:48.240 --> 0:02:51.200 really connectivity between the two. I think it was like 0:02:51.240 --> 0:02:54.320 a was it an interview on data transmission? I can't 0:02:54.320 --> 0:02:56.480 remember me it was linked to on data transmission UM 0:02:56.760 --> 0:02:59.600 that code out UK where someone asked him about in 0:02:59.639 --> 0:03:04.600 Cariboo was like you know math, yeah, math, math, different things. 0:03:05.400 --> 0:03:08.720 So it's kind of disappointing. You can imagine the the interviewers, 0:03:08.880 --> 0:03:11.680 you know, kind of slumping down, you know when he 0:03:11.840 --> 0:03:15.040 got that answer. But other ones are Garfuncle had a 0:03:15.040 --> 0:03:17.640 master's degree in mathematics, which I was not aware of. 0:03:17.800 --> 0:03:19.919 I wasn't. I was surprised by that one. Yeah, I mean, 0:03:19.960 --> 0:03:22.840 certainly his hair seems to indicate some sort of like 0:03:23.040 --> 0:03:27.919 science lab type situation. But but no, he and again 0:03:27.960 --> 0:03:30.320 I can't think of any Garfuncle songs where where I 0:03:30.320 --> 0:03:32.600 have listened to him and be like, wow, bright Eyes 0:03:32.680 --> 0:03:36.000 is such a mathematical song, you know. And again maybe 0:03:36.000 --> 0:03:41.320 I'm I'm missing the finer corners of his discography, but yeah, um. 0:03:41.360 --> 0:03:44.320 And then another one that comes to mind, uh is 0:03:44.640 --> 0:03:47.680 a chat by the name of Rupert Way, who DJ 0:03:47.840 --> 0:03:50.400 is under the name dj Irk. Yeah, and I actually 0:03:50.440 --> 0:03:53.720 interviewed him for the blogs a little while back, and uh, 0:03:53.800 --> 0:03:57.640 he has like a PhD in uh, some kind of 0:03:57.680 --> 0:04:00.840 type of mathematics that dynamic systems something. It kind of 0:04:01.440 --> 0:04:03.640 it just goes right over my head when when he 0:04:03.680 --> 0:04:06.640 told me what it was. But but yeah, And there're 0:04:06.680 --> 0:04:08.360 just a few there. Do you have any that I'm 0:04:08.440 --> 0:04:11.040 leaving off? No, No, that that sounds Um, those are 0:04:11.080 --> 0:04:12.440 some of the big ones, I think. And I was 0:04:12.480 --> 0:04:15.840 I was actually revisiting your interview with him, and he 0:04:15.920 --> 0:04:19.599 was talking. You were asking him about the connection between 0:04:19.640 --> 0:04:23.000 Mathew music and I think he was saying that he 0:04:23.040 --> 0:04:26.040 doesn't it doesn't really help anymore than it does with 0:04:26.040 --> 0:04:31.279 what he says, say around trip a trip around the supermarket. 0:04:31.000 --> 0:04:35.240 I've obviously taken that out of context. Uh, but he 0:04:35.279 --> 0:04:39.000 did say something about mental agility, good memory, good numerous 0:04:39.080 --> 0:04:41.120 e and a lot of determination, he says, or what 0:04:41.200 --> 0:04:44.360 really counts. And although these are math related I'm quoting him, 0:04:44.600 --> 0:04:48.080 they are not math specific. There are lots of overriding 0:04:48.160 --> 0:04:52.480 instinctive and emotional factors too, which I thought was interesting 0:04:52.600 --> 0:04:56.200 because he's he's sort of saying, yeah, all of this helps, 0:04:56.279 --> 0:04:59.720 but it does not make you a musician per se, 0:05:00.000 --> 0:05:02.560 because there are some factors that you just can't that 0:05:02.680 --> 0:05:05.560 don't fit into the mathematical model, so to speak. Right. Yeah, 0:05:05.600 --> 0:05:09.320 his answer was far more insightful than caribous. Yeah, yeah, yeah, 0:05:09.760 --> 0:05:12.560 he actually he went on to say some very interesting stuff. Actually, 0:05:12.600 --> 0:05:14.680 So if you haven't checked out Robert's blog on that 0:05:15.120 --> 0:05:18.200 with with dj Oric, should definitely check that out. Yeah yeah, 0:05:18.200 --> 0:05:21.520 I'll throw the link up. But but yeah, you end 0:05:21.640 --> 0:05:23.719 up in the in this this situation where the the 0:05:23.760 --> 0:05:26.719 answer is kind of yeah, kind of yeah, but also 0:05:27.480 --> 0:05:31.480 not really um and and there's no real firm answer 0:05:31.480 --> 0:05:36.080 because I mean, when you break it down, UM, I 0:05:36.080 --> 0:05:38.440 mean we we've discussed in the past, like mathematics, what 0:05:38.600 --> 0:05:41.200 is it is the human invention that just is so 0:05:41.279 --> 0:05:44.520 clever that it describes everything in the universe? Or is 0:05:44.560 --> 0:05:48.039 it a discovery? Did we find the secret language of 0:05:48.040 --> 0:05:51.040 the universe and we're so awesome because we found it? Again, 0:05:51.200 --> 0:05:54.080 humans end up looking pretty awesome. Either way, you spend 0:05:54.080 --> 0:05:57.599 that but if but but but either way, you're talking 0:05:57.640 --> 0:06:02.000 about a system of numbers that can describe everything. So 0:06:02.120 --> 0:06:03.719 it stands to reason that it would be able to 0:06:03.720 --> 0:06:07.520 describe music, right, Right, And yes, so there are definitely 0:06:07.560 --> 0:06:09.719 some similarities with that because you would ask the same 0:06:09.720 --> 0:06:11.839 thing about music in a sense, right, it is music 0:06:11.920 --> 0:06:14.120 something that we discovered is just sort of inherent in 0:06:14.120 --> 0:06:17.800 in us. And then we've talked about even our fingers before, Right, 0:06:17.839 --> 0:06:20.320 we've got five fingers on each hand, and how that's 0:06:20.360 --> 0:06:22.640 determined our currency in the way that we count in 0:06:22.720 --> 0:06:26.080 number systems, and same thing with music. It's it's determined 0:06:26.080 --> 0:06:29.440 the way that we have, Uh, created scales, and we 0:06:29.640 --> 0:06:33.839 created instruments. Yeah, like strings vibrated a certain frequency and 0:06:33.880 --> 0:06:36.919 you can measure those mathematically. Sound waves can also be 0:06:36.960 --> 0:06:40.120 described by mathematical equations. Uh. I mean it comes down 0:06:40.120 --> 0:06:43.080 to like scientists of any discipline, they use mathematics to 0:06:43.160 --> 0:06:49.040 describe the physical world. Changing physical world of movable opjects, 0:06:49.560 --> 0:06:54.880 and they predict the outcome of physical process, so you 0:06:54.920 --> 0:06:57.799 know there's gonna be some cross over there. But then again, 0:06:57.839 --> 0:07:00.000 an equation is not going to be able to describ 0:07:00.040 --> 0:07:03.480 have a piece of music, and uh, I mean there 0:07:03.480 --> 0:07:07.320 are a certain mathematical well, well you can there are 0:07:07.360 --> 0:07:10.360 equations that can describe some of the mathematical structures that 0:07:10.400 --> 0:07:12.680 are inherent in music, but you're not going to be 0:07:12.760 --> 0:07:14.960 able to like to say, um, yeah, I want to 0:07:14.960 --> 0:07:18.360 listen to that. Um, you know that can concerto by 0:07:18.720 --> 0:07:20.320 so and so, But I don't have time for the 0:07:20.360 --> 0:07:23.960 full thing. Just send me the equation. Well, and it's 0:07:23.960 --> 0:07:27.880 interesting too, because the each equation you could interpret in 0:07:27.880 --> 0:07:31.040 a different way as a musician, right yeah. But I 0:07:31.040 --> 0:07:33.600 mean so there's that's the part of it that's like, well, okay, 0:07:33.600 --> 0:07:37.320 here's here's the precise language. Um that you know, and 0:07:37.560 --> 0:07:43.360 again drawing parallels to math, Math has a universal precise language. Right. 0:07:43.680 --> 0:07:46.600 But once you know, you give this equation of music 0:07:46.640 --> 0:07:49.560 to someone, they might perform it in a completely different 0:07:49.600 --> 0:07:52.640 way or take liberties with it that you wouldn't necessarily 0:07:52.680 --> 0:07:56.880 see in math. But again again talking about similarities, Um, 0:07:57.160 --> 0:07:59.880 both disciplines gravitate towards symmetry. Right. You see this in 0:08:00.080 --> 0:08:04.280 music all the time. Um, of course there's there's cacophony, right, 0:08:05.440 --> 0:08:08.520 Uh yeah, noise music and all that. I mean that's 0:08:08.560 --> 0:08:10.280 the thing too. It's like music when you're talking about 0:08:10.280 --> 0:08:11.800 like what is music? Yeah, there's some there are there 0:08:11.920 --> 0:08:14.760 certain types of music that are very mathematical sounding, and 0:08:14.840 --> 0:08:17.400 you can break down you can you know, apply some 0:08:17.400 --> 0:08:20.040 some number to the numbers to the music theory of 0:08:20.040 --> 0:08:22.000 it all, and it makes perfect sense. But then you 0:08:22.200 --> 0:08:24.600 pull out some sort of like noise artist where they're 0:08:24.680 --> 0:08:28.280 using very abstract sounds music that uh, to quote my wife, 0:08:28.360 --> 0:08:32.360 sounds like someone through a xylophone down a stairwell. And 0:08:32.800 --> 0:08:35.520 then it's gonna be hard to say like, oh, well, mathematically, 0:08:35.559 --> 0:08:38.800 this is what's going on there. But then again, you 0:08:38.800 --> 0:08:42.000 could also make the counter argument that even a chaotic system, um, 0:08:42.040 --> 0:08:45.400 there's math going on there. Can you can go back 0:08:45.400 --> 0:08:48.400 and forth. And now the ancient Greeks they definitely thought 0:08:48.400 --> 0:08:51.160 there was there were numbers tied up in music, that 0:08:51.320 --> 0:08:54.840 math and music were very closely related. Is this uh 0:08:55.000 --> 0:08:59.200 pithe Pythi versus yeah, yeah, yeah, like because he use 0:08:59.200 --> 0:09:01.360 all about the ratio of yeah, yeah, and his his 0:09:01.400 --> 0:09:05.920 whole like system of of education. Um. They considered music 0:09:05.960 --> 0:09:09.000 to be a strictly mathematical disciple in involving number of relationships, 0:09:09.080 --> 0:09:11.560 ratios and proportions, and so if you break it down, 0:09:11.600 --> 0:09:15.839 it would basically be a subdivision to quantitative mathematics in 0:09:16.880 --> 0:09:22.080 Pithagorean time. So yeah, harmonica ratios proportions central in the 0:09:22.120 --> 0:09:26.360 Greek's understanding too musical, okay, yeah, And so just to 0:09:26.360 --> 0:09:28.040 back up a little bit to the five tone or 0:09:28.040 --> 0:09:31.160 the pentatonic scale developed about three thousand years ago in China, 0:09:31.640 --> 0:09:35.880 and then the Greeks they have the seven tone scale, right, um. 0:09:35.920 --> 0:09:39.040 And then then we're talking about the twelve tone scale, right, 0:09:39.040 --> 0:09:41.840 And this is when we're talking about Pythagora is really 0:09:41.880 --> 0:09:44.680 obsessing on these ratios. And I won't go into the 0:09:44.720 --> 0:09:46.880 math behind it, but that's how we sort of came 0:09:46.960 --> 0:09:50.400 up with these varying skills. And it wasn't till around 0:09:50.480 --> 0:09:53.160 I think Box time where they took one of those 0:09:53.280 --> 0:09:55.679 ratios that was a bit off and and tinkered with 0:09:55.720 --> 0:09:59.400 it and they came up with the final twelve tones. Um. 0:09:59.520 --> 0:10:03.240 So again there's there's a system behind there. There's math 0:10:03.360 --> 0:10:07.240 that's driving the way that we are expressing music, which 0:10:07.280 --> 0:10:10.560 is pretty interesting, all right, But what exactly is going 0:10:10.559 --> 0:10:14.120 on in the brain? Right? Yes? Yes, so let's uh, 0:10:14.200 --> 0:10:16.120 let's take a quick break, and when we come back, 0:10:16.240 --> 0:10:18.920 we will look at math and music in the human mind. 0:10:24.080 --> 0:10:27.600 This presentation is brought to you by Intel sponsors of tomorrow, 0:10:32.160 --> 0:10:39.240 and we're back music brains. What's happened? Yes, um, so, 0:10:41.080 --> 0:10:44.680 obviously scientists have looked at the brain and analyze what 0:10:44.760 --> 0:10:47.480 exactly is going on when we think about music or 0:10:47.600 --> 0:10:52.360 contemplate music versus contemplating math, and they have Scientists actually 0:10:52.360 --> 0:10:55.240 looked at brain injuries that suggest a single region in 0:10:55.280 --> 0:10:58.320 the left hemisphere of the brain gives rise to sequential 0:10:58.360 --> 0:11:02.280 analytic processing, which is used for both doing algebra and 0:11:02.320 --> 0:11:05.120 reading music. All right, But then on the other hand, 0:11:05.120 --> 0:11:07.000 there was a two thousand eight study from the University 0:11:07.000 --> 0:11:12.080 of Arkansas that used a human Information Processing Survey instrument 0:11:12.160 --> 0:11:16.480 or a HIPS instrument to measure hemispheric collaterality. They used 0:11:16.480 --> 0:11:18.720 a hundred and one participants asked them to discuss their 0:11:18.720 --> 0:11:21.520 prowess in first math and then in music, and their 0:11:21.600 --> 0:11:25.920 finding suggested that math is a left hemisphere preference and 0:11:26.000 --> 0:11:30.640 music is a right hemisphere preference. Okay, well, it's interesting, 0:11:30.760 --> 0:11:33.320 right because we've talked about music before and how it 0:11:33.360 --> 0:11:35.560 affects the brain, and we've found that there is no 0:11:35.720 --> 0:11:38.800 one music center, um, so it's sort of spread up 0:11:38.840 --> 0:11:41.640 throughout the brain. But to to know that's obviously engaging 0:11:41.679 --> 0:11:43.840 in a part of the brain that is that's tracking 0:11:44.200 --> 0:11:47.599 um math is interesting. And likewise, there have been a 0:11:47.679 --> 0:11:50.720 number of studies which sort of say different things about 0:11:51.240 --> 0:11:57.160 exactly how musical education affects one's mathematical prowess. Um. They 0:11:57.200 --> 0:11:59.280 have been studies they've found that people with musical training 0:11:59.320 --> 0:12:03.199 outperform people who don't have musical training. Um. But then 0:12:03.240 --> 0:12:05.600 there's uh, there's stuff like for instance, there was the 0:12:05.920 --> 0:12:09.320 Montreal Montreal Piano Project. All right, half the children were 0:12:09.360 --> 0:12:11.920 giving piano lessons for three years, and after two years, 0:12:12.280 --> 0:12:16.280 the piano playing kids were outscoring the others on spatial ability. 0:12:16.640 --> 0:12:20.319 So the argument here was that yeah, learning music helps you, 0:12:20.760 --> 0:12:23.600 um helps you with math because it's reinforcing the brain 0:12:23.640 --> 0:12:26.960 circuits that power spatial thinking, which comes in handy not 0:12:27.040 --> 0:12:29.600 only for knowing what keys match up with what note, 0:12:29.920 --> 0:12:33.800 but also in geometry, physics, and chemistry, all right, But 0:12:33.840 --> 0:12:37.920 then opposing that we have um um a study from 0:12:37.960 --> 0:12:41.640 the University of Toronto. Uh, and this one, this one 0:12:41.679 --> 0:12:44.400 was pretty cool too. They took six year olds, all right, 0:12:44.960 --> 0:12:48.280 and they took weekly piano and singing lessons throughout the 0:12:48.320 --> 0:12:51.840 school year, and they exhibited an average i Q increase 0:12:51.880 --> 0:12:55.520 of seven h point zero points. Right. The other six 0:12:55.600 --> 0:12:58.520 year olds who took either weekly drama lessons or received 0:12:58.520 --> 0:13:01.800 no extra trick curricular lessons displayed an average i Q 0:13:02.040 --> 0:13:06.079 rise of four point three points. So that's another one 0:13:06.080 --> 0:13:08.760 that also seems to indicate, all right, they're they're learning 0:13:08.880 --> 0:13:11.560 music and this is helping them with their scores. But 0:13:11.800 --> 0:13:15.040 I also think, like non scientifically, that maybe the drama 0:13:15.080 --> 0:13:17.640 kids were just having more fun and didn't have as 0:13:17.720 --> 0:13:21.280 much time to really play with the studying all that much. Huh, 0:13:21.360 --> 0:13:24.720 all right, yeah, they were too busy emoting. And then 0:13:24.760 --> 0:13:26.360 the kids who didn't get anything, they were just setting 0:13:26.360 --> 0:13:30.000 around in study hall like destroying desks with tiny axes 0:13:30.080 --> 0:13:32.760 or something. They weren't having new experiences. And we just 0:13:32.760 --> 0:13:35.480 talked about this so important is that you need to 0:13:35.480 --> 0:13:38.280 to have new experiences in order to create new pathways. Yeah, 0:13:38.400 --> 0:13:42.680 discussed in our Einstein's Brain podcasts. Alright, so there's there's 0:13:42.720 --> 0:13:47.760 some basis here for some some waltzing, let's say, between 0:13:48.280 --> 0:13:51.520 between the brain and music and maths. What I was 0:13:51.720 --> 0:13:55.280 interested in knowing was whether anybody had ever actually taken 0:13:55.720 --> 0:13:59.480 a piece of music and said, okay, here's here's here's 0:13:59.480 --> 0:14:02.240 some math right here, right, because there are certain pieces 0:14:02.280 --> 0:14:03.800 of music that I hear sometimes and I'm like, god, 0:14:03.840 --> 0:14:07.040 I can I can't. Maybe geometrically, I can see things 0:14:07.200 --> 0:14:10.160 going on in this music, um, which is sort of 0:14:10.200 --> 0:14:11.800 interesting way you're talking about in your mind, not the 0:14:12.360 --> 0:14:15.520 not the visualizer that pops up, yeah, exactly, not in 0:14:15.520 --> 0:14:17.520 front of my computer with you know, I don't have 0:14:17.600 --> 0:14:22.720 like purple splashes. Um. But what I found was that 0:14:22.760 --> 0:14:25.960 there is a book called meta Magical Femus. It's called 0:14:26.040 --> 0:14:28.760 Questing for the Essence of Mind and Pattern by Douglas 0:14:28.760 --> 0:14:32.040 host Daughter And he actually looked at Chopin's music and 0:14:32.160 --> 0:14:35.000 box as well, but he said, Chapon's music is filled 0:14:35.040 --> 0:14:38.200 to the brim that I'm quoting with algebra algebraic tricks 0:14:38.200 --> 0:14:41.360 of cross rhythm. A famous example is in his iconoclastic 0:14:41.360 --> 0:14:44.640 waltz Opus forty two in a flat major written eighteen 0:14:44.720 --> 0:14:48.920 forty and this waltz. The baseline follows the usual oompapa 0:14:49.320 --> 0:14:57.280 convention of the waltz. I don't know if papa, yeah nice, yeah, okay, okay, 0:14:57.320 --> 0:14:59.840 But the melody of the first section completely counters this 0:15:00.040 --> 0:15:03.960 three nuts. It's six six eighth notes. Instead of being 0:15:03.960 --> 0:15:06.080 broken up into three pairs aligned with the left hand 0:15:06.320 --> 0:15:10.080 bounces while playing form two triplets. The initial notes of 0:15:10.120 --> 0:15:12.960 the success of triplets are to be clearly emphasized and prolonged, 0:15:13.000 --> 0:15:16.160 thus creating a higher level melody abstracted out of the 0:15:16.320 --> 0:15:20.640 quietly rippling right hand. Yeah. I think I'm gonna have 0:15:20.640 --> 0:15:23.040 to hear an example and put that together. Yes, yes, 0:15:23.080 --> 0:15:25.960 And he's saying that this melody is composed of two 0:15:26.000 --> 0:15:28.400 notes per measure beating regularly against three notes of a 0:15:28.440 --> 0:15:30.800 waltzing base. And he says it's a marvelous trump let 0:15:30.920 --> 0:15:34.880 aier effect, which which means the oral equivalent to an 0:15:34.880 --> 0:15:38.640 optical illusion. Basically, So let's take a quick listen to 0:15:39.680 --> 0:15:43.240 uh this waltz. It was forty two in a flat major. 0:15:53.680 --> 0:15:56.800 I don't know, did you hear it? Um? Yeah, I 0:15:56.880 --> 0:15:59.000 think I can. I can get a sense of some 0:15:59.080 --> 0:16:02.920 of that coming together. I definitely got the oom Papa. Yes. 0:16:03.400 --> 0:16:06.280 So that's one example where someone has actually tried to 0:16:06.320 --> 0:16:10.560 map this, which is kind of interesting. And um. There 0:16:10.600 --> 0:16:14.160 was another example that I found by mathematician Hence Strob, 0:16:14.200 --> 0:16:16.640 and he talks about modal jazz. And the reason I 0:16:16.760 --> 0:16:19.960 really wanted to look into this is because jazz modal 0:16:20.040 --> 0:16:23.880 jazz is uh is someone like uh, it was like 0:16:24.360 --> 0:16:29.680 Miles Davis. Miles Davis is usually attributed to be the 0:16:29.720 --> 0:16:32.640 person that that sort of creative medal jazz are popularized 0:16:32.680 --> 0:16:36.800 it um, particularly in the fifties. So this modal jazz 0:16:36.880 --> 0:16:39.960 is is said to have a more horizontal structure, whereas 0:16:39.960 --> 0:16:43.720 traditional jazz is structured more vertically, and modal just means 0:16:43.720 --> 0:16:45.040 that he took a bunch of notes and he sort 0:16:45.040 --> 0:16:49.000 of squished them all in this my my horrible understanding 0:16:49.040 --> 0:16:53.280 of both mathematics and UM and music theory. Um. So 0:16:53.400 --> 0:16:55.760 it just seems weird that jazz would like I thought 0:16:55.840 --> 0:16:58.920 jazz was free flowing, man. I thought you can't put 0:16:59.000 --> 0:17:02.600 math on jazz. Jazz as its own rhythm. Yeah, well 0:17:02.640 --> 0:17:05.520 that's the incredible thing. And that's why I love Miles 0:17:05.600 --> 0:17:08.240 Davis is because it does seem like there's a lot 0:17:08.280 --> 0:17:12.560 of um sort of off off the cuff playing, right, 0:17:13.040 --> 0:17:14.639 But I mean, the fact of the matter is is 0:17:14.680 --> 0:17:19.560 that they're taking some some very um concentric like rhythms 0:17:19.960 --> 0:17:21.960 and then they're playing off of that. So what you 0:17:22.040 --> 0:17:24.240 might hear which sounds sort of like, oh wow, man, 0:17:24.280 --> 0:17:28.040 that that cat is just going nuts on the saxophone, Um, 0:17:28.119 --> 0:17:30.360 they are, but but they're doing it in the sort 0:17:30.400 --> 0:17:33.359 of loops, um, these horizontal loops, and they're not doing 0:17:33.400 --> 0:17:36.080 a lot of key changes. So let me try tokay. So, like, 0:17:36.400 --> 0:17:39.639 if you had like a really crazy story that that 0:17:39.640 --> 0:17:42.560 that at its heart followed a traditional story arc, even 0:17:42.560 --> 0:17:44.959 if it involved like art arts from Mars in love 0:17:45.040 --> 0:17:47.359 with each other or something. Yeah, yeah, And everybody knows 0:17:47.400 --> 0:17:50.360 that that once you start, you know, to be good 0:17:50.359 --> 0:17:52.719 at any craft, right, you have to know the absolute basics. 0:17:52.760 --> 0:17:55.040 You have to master it. And um, you know, Myles 0:17:55.040 --> 0:17:58.480 Savis is someone who certainly was master at what he did, 0:17:58.920 --> 0:18:01.320 So that gave him the othery to sort of riff 0:18:01.359 --> 0:18:04.840 off of stuff and um, play with modal notes and 0:18:04.840 --> 0:18:06.719 and do all these sort of different things that actually 0:18:06.800 --> 0:18:10.840 changed people's perception of that music itself. So what I 0:18:10.840 --> 0:18:13.560 thought was interesting about it is that this this guy Hendstrub, 0:18:13.640 --> 0:18:16.280 he talks about the traditional jazz being structured more vertically, 0:18:16.280 --> 0:18:19.800 which means in this context that traditional jazz impro improvisations 0:18:19.800 --> 0:18:23.480 are based on chord progressions and modal jazz. On the 0:18:23.520 --> 0:18:28.120 other hand, improvised improvisations typically go on for long periods 0:18:28.160 --> 0:18:30.520 without any chord change. So that so I was talking 0:18:30.520 --> 0:18:33.480 about earlier, and the interest is more turned towards the 0:18:33.480 --> 0:18:37.879 melodic line. Uh So, it's it's a That's why I 0:18:37.880 --> 0:18:39.280 thought it was sort of interesting to me because I 0:18:39.280 --> 0:18:41.280 thought I can see that visually. I can see that 0:18:41.280 --> 0:18:44.560 in Miles Davis's music. You can see this horizontal spreading. 0:18:44.560 --> 0:18:46.400 You can see in Yo yo mom when he does 0:18:47.200 --> 0:18:50.720 uh the box suitets um. You can see it maybe 0:18:50.720 --> 0:18:52.879 even in like PJ. Harvey and like White Chalk, like 0:18:52.920 --> 0:18:55.119 the Cults an album that has sort of like this 0:18:55.359 --> 0:18:58.800 horizontal spreading, although you could say there are some there's 0:18:58.840 --> 0:19:02.280 some vertical loops of coophany in that as well. But anyway, 0:19:02.359 --> 0:19:05.920 let's let's just listen to a quick clip from kind 0:19:05.920 --> 0:19:21.680 of Blue Miles Davis. Cool. Yeah, Now, did you say 0:19:21.760 --> 0:19:25.399 this is actually your favorite track, your favorite song, favorite album? 0:19:25.440 --> 0:19:28.560 I mean the entire album is my favorite. There's actually 0:19:28.600 --> 0:19:30.560 not one song on there that I would say that 0:19:30.600 --> 0:19:32.760 is my absolute favorite. I love it as a whole piece, 0:19:33.040 --> 0:19:35.680 and um, you know we've talked about this before and 0:19:35.920 --> 0:19:38.159 getting in the zone, and um, this is one of 0:19:38.160 --> 0:19:41.239 those pieces of music that I can listen to and 0:19:41.320 --> 0:19:43.000 it does sound it kind of put me into a 0:19:43.040 --> 0:19:46.359 different state that allows me to think clearer, think at 0:19:46.440 --> 0:19:49.159 higher levels. I think, is why I like it. And 0:19:49.200 --> 0:19:51.560 also we've talked about this too, like lyrics sometimes bother 0:19:51.720 --> 0:19:56.640 me when I'm trying to cogitate up in Monogaen. So 0:19:56.800 --> 0:19:59.520 you know, that's that's that's some of the discovery here 0:19:59.600 --> 0:20:01.639 where we're seeing that the music and the math, at 0:20:01.680 --> 0:20:04.000 least again geometrically, I can see it. I don't know 0:20:04.040 --> 0:20:06.320 if it's the same for other people. But there's a 0:20:06.320 --> 0:20:09.240 guy named Dave Russ, and he's associate professor of mathematics 0:20:09.320 --> 0:20:12.879 at Northern Illinois University, and he really does try to 0:20:12.960 --> 0:20:16.520 make this correlation between music and math, and he thinks 0:20:16.520 --> 0:20:20.640 it's important for for students to better understand math. In fact, well, 0:20:20.720 --> 0:20:24.439 he says mathematics, like music, embodies certain patterns and ideas 0:20:24.480 --> 0:20:30.600 which don't translate well into words, as we found out. Uh, 0:20:30.960 --> 0:20:33.440 as you listener, hath end up. We can feel them, 0:20:33.480 --> 0:20:36.760 see them, understand them, but only after we have really 0:20:36.840 --> 0:20:39.399 worked to lift them off the paper and into our minds, 0:20:39.720 --> 0:20:41.960 only after we've tried to see where they come from, 0:20:42.080 --> 0:20:47.480 only after considerable practice with the minutia, gradually adding the trills. Uh, 0:20:47.520 --> 0:20:50.280 do we have the full spirit of the idea? Mathematics 0:20:50.280 --> 0:20:53.359 like music as a human adventure, people create and discover it, 0:20:53.680 --> 0:20:56.480 they try to then share it and enjoy it. Yeah. 0:20:56.640 --> 0:20:58.320 I mean I I definitely found that to be the 0:20:58.320 --> 0:21:01.320 case with both music and mathematics, because on one hand, 0:21:01.400 --> 0:21:05.600 I love um certain genres of music, and I'll you know, 0:21:05.640 --> 0:21:07.600 I'll listen to it all the time, but I'm not 0:21:07.640 --> 0:21:10.280 necessarily really good at describing what's great about it. Like 0:21:10.320 --> 0:21:11.920 if if I'm like, you know, talking to a friend, 0:21:11.960 --> 0:21:13.600 I'm like, oh, you gotta listen to this new mix 0:21:13.640 --> 0:21:14.920 by so and so, and they might be like, well, 0:21:14.920 --> 0:21:17.080 what's awesome about it? And I may be a little 0:21:17.080 --> 0:21:19.040 stump for words, you know, unless I have some time 0:21:19.080 --> 0:21:23.400 to prep. Likewise, with mathematics, I was the last week 0:21:23.400 --> 0:21:26.359 I was working on an article about number theory and 0:21:26.400 --> 0:21:30.200 like number theory. Especially when writing for a general audience 0:21:30.320 --> 0:21:34.719 and a you know, non math audience, it's it quickly 0:21:34.800 --> 0:21:39.120 becomes a conversation that cannot be really held in English 0:21:39.200 --> 0:21:41.320 but needs to be held or any language, but needs 0:21:41.320 --> 0:21:43.840 to be held in math. You know, it needs to 0:21:43.840 --> 0:21:47.240 be held with numerals and and equations. So it becomes 0:21:47.240 --> 0:21:51.199 increasingly difficult to to explain the topic without being the 0:21:51.240 --> 0:21:54.680 topic right right. And that's why us wildly humans, I suppose, 0:21:54.840 --> 0:21:57.480 turned to math and music to try to express ourselves 0:21:57.480 --> 0:22:00.240 and our ideas and in a better way. Yeah, because 0:22:00.359 --> 0:22:02.320 I think I saw it pointed out that both both 0:22:02.400 --> 0:22:05.359 music and math are like they're self describing things. The 0:22:05.440 --> 0:22:10.200 music describes itself, the math describes itself, and h and yeah, 0:22:10.240 --> 0:22:11.879 at the at the end of the day, it kind 0:22:11.880 --> 0:22:14.159 of sounds like, you know, defeatist, but they both kind 0:22:14.160 --> 0:22:18.119 of described themselves the best. There we go looking in 0:22:18.160 --> 0:22:22.720 the mirror. I'm trying to change the world. I don't 0:22:22.760 --> 0:22:25.919 know I was trying to do, Michael Jackson, there apologize 0:22:26.760 --> 0:22:29.280 you were trying to do like an impersonation. I was 0:22:29.320 --> 0:22:31.800