Matt: 0:14

Hello everyone And welcome to the switch statement podcast It's a podcast for investigations into miscellaneous tech topics

geb_matt_ch1_p1: 0:30

Hey, John, how are you doing?

jon_raw: 0:32

Matt, I'm doing pretty darn good. How you doing?

geb_matt_ch1_p1: 0:36

I am doing all right.

jon_raw: 0:38

So we have switched gears almost, I want to say completely

geb_matt_ch1_p1: 0:43

Diametrically opposed.

jon_raw: 0:46

diametrically opposed indeed between Masters of Doom, which was kind of like a light snack, you know, just some like toilet reading type thing, not to denigrate it. It was a great book, but it's very easy to read. Action packed, had a great narrative. We're switching to a book called Gödel, Escher, Bach, which

geb_matt_ch1_p1: 1:06

a textbook,

jon_raw: 1:07

it is practically a textbook.

geb_matt_ch1_p1: 1:10

in, in a weird, in a very weird way. It's good. It's hard to pin down.

jon_raw: 1:15

Yes. I feel like we're entering the mind of the author. Like he's kind of, he's somehow like regurgitating his own brain onto the pages of this book.

geb_matt_ch1_p1: 1:25

Yeah, we are kind of in this stormy realm where you'll just see Bach just kind of appear and out of nowhere. Um,

jon_raw: 1:33

exactly.

geb_matt_ch1_p1: 1:34

Escher is in the corner looping strangely.

jon_raw: 1:38

his own self, looking into some sort of reflective object.

geb_matt_ch1_p1: 1:42

Yeah. And they are forming the eternal golden braid,

jon_raw: 1:47

Yeah,

geb_matt_ch1_p1: 1:47

which has he explained? Has he explained that?

jon_raw: 1:51

I don't think so. I, I'm trying to remember if Braid was even mentioned. He might've mentioned Braid to, to describe these recursive, like, I feel like a huge theme in this book is recursion, self reference, you know, it's things that somehow manifest themselves. Within their own either description or, um, well, we'll discuss a bunch of examples, just now realizing it's hard to think of examples off the top of the dome for that kind of thing. But so I think that's what a braid is, is sort of this like set of self references that goes infinitely deep or

geb_matt_ch1_p1: 2:28

Right. Right.

jon_raw: 2:30

but anyhow, this first chapter is very much an intro to the material. And he, he decided to discuss the three main subjects of the book in this first chapter. Uh, but he discussed them in reverse order, which I thought was interesting. He starts with Bach.

geb_matt_ch1_p1: 2:47

They're almost more like muses. I feel like for the, like, you know, they, they obviously, Oh, there's a code in this book. I don't know. I just was scrolling through the, uh, through the list of illustrations and there's some sort of crazy, like glyphs. I've never seen anything like that. Um, but

jon_raw: 3:09

We're going to have to solve that.

geb_matt_ch1_p1: 3:10

have to solve that. Yeah. Um, but yes, um, So we were talking about, yeah, like Bach and, uh, Girdle. I think I'm just going to say Girdle. I know that's not right, but I think it's the closest that my American palate can, and I'm just going to fail if I try to say it actually how it's supposed to be said. So,

jon_raw: 3:32

Yeah. We are not good at pronouncing names. So if we mispronounce names, it's not intentional and we apologize.

geb_matt_ch1_p1: 3:38

Yeah, so yeah, he introduces our kind of, our cast of, or at least our inspirations for this book. And we start with Bach.

jon_raw: 3:46

Yes, in the court of Frederick the Great, which, oh man, I don't even know what he was the monarch of. Was it like Austria or something? Prussia. Okay. So a non existent, a thing that turned into, uh, like Germany and

geb_matt_ch1_p1: 4:00

Yeah.

jon_raw: 4:01

Uh, so anyway, Frederick the Great, a King, I guess, well known for his appreciation of music. He himself was a flautist. Yep. So he, he's in power. Bach was actually an old man at this point. So had already had a totally illustrious career. One of the longest and most productive careers in musical history. Bach's own offspring, Carl Philip Emanuel, I think was the court musician. And Frederick the Great invited Bach to court, you know, Bach senior. Um, he invited him to court to kind of mess around and play some music.

geb_matt_ch1_p1: 4:38

Yeah, he's, he is 62 at this point, Bach. So, um, which, I mean, in 1747, it's a pretty good run. there's an interesting point here, like, Yeah, this did just have this kind of, um, I mean, I guess it's not medieval, but like just monarchies are weird. And you could like come to a town and then just the king is like, get on down here. I, you can't even shower. You gotta come and play, play music for me. And then he was like, yeah, let's do it. He was like, it just like, Sheerly, like, absolutely. Sorry, we're

jon_raw: 5:16

Yes. No, no, that's fine. You have to be such a sycophant, too. Like, I was The letter that Bach ended up writing to Frederick, sort of after the fact, was so cringey. In how, like Just deferential. Yeah, effusive and like, oh, I'm not even worthy to like walk in the same room as you. And it's like, dude, you're fucking Bach. Like, who the hell is Frederick the Great? Like, you

geb_matt_ch1_p1: 5:41

Yeah. No one remembers Frederick the Great.

jon_raw: 5:44

Yeah, so. There's some like history buff out there that's like shaking his fist at us right

geb_matt_ch1_p1: 5:50

but you could tell, you could tell that, uh, Frederick, uh, or King Frederick was fangirling over, over Bach. You know, he was like, he was pretty, he was pretty excited that he was there.

jon_raw: 6:03

Oh yeah. I mean, can you imagine being a music appreciator of the day where, I mean, Bach being a 62 year old man, Frederick the Great probably grew up with Bach's pieces, all of his, you know, amazing, well known pieces. And now here he is in the flesh. I mean, that's literally meeting your hero. So, um, hopefully Frederick the Great had a good time.

geb_matt_ch1_p1: 6:25

So, um, I, I would say the, like, there's, there's a lot of, I mean, as, as the listener can probably tell, they don't go into a lot of detail about the historical context of this interaction, uh, and what have you. But there's the nugget here ultimately is that Bach writes, he, while he's there. He improvises a, is it a canon or a fugue? Uh, I've, I've, I'm mixing these up,

jon_raw: 6:54

Yeah. So my, my take is a Canon is kind of the simpler version of a few. A Canon is like a simple theme that plays over itself. Like row, row, row your boat. Um, a few guy on the other hand is a similar idea, but it has a lot more musical flexibility where you can have like, you know, counterpoint, which I used to refer to as contrapuntal because that's what they call it. If you're learning music. Um, and, and you can have different melody, you know, you can basically quote unquote, play jazz with it a little bit more. So I think musical offering, uh, is a fugue,

geb_matt_ch1_p1: 7:35

Yeah.

jon_raw: 7:36

but maybe what he played for Frederick, cause my understanding is like, he did this extemporaneous riff, like you're saying, but then he like went home and perfected it. And that's what musical offering is.

geb_matt_ch1_p1: 7:48

Exactly. Exactly. And if the listeners are not familiar with the word extemporaneous, because I was not, it's basically like he was improvising.

jon_raw: 7:57

Yeah.

geb_matt_ch1_p1: 7:58

he uses the word extempore like as a verb, but, uh,

jon_raw: 8:04

Yeah, which I had not seen that usage of it, but, but yeah, which, and, and the author and I agree with this, I mean, having played, like I grew up playing classical music on the piano, so I played a ton of Bach music and his music is hard to play because it's, you're playing one thing with the right hand and you're like often playing a different melody with the left hand. So it's not like you're just playing some rhythm with the left hand where you can kind of. Getting the flow of it and then like kind of ignore it and focus on the right hand. So very difficult to play. And here Bach is just like inventing something on the spot. Like, I think it's just a testament to his musical prowess.

geb_matt_ch1_p1: 8:43

Yeah. Um, but in this musical offering, and that's, that's actually the name of it. There is a piece where Bach is gradually increased, like raising the key in such a way that you could continue to play it forever. And, and to the listener, it would sound like you were constantly Going up, you know, up in key, but actually it, you know, he, he pulls a clever trick where he can kind of like bring it back down, like, and, but it always sounds like you're moving up.

jon_raw: 9:17

Yeah.

geb_matt_ch1_p1: 9:18

and this is, this is kind of how it ties back to this concept of like, uh, strange loops. Cause he's, he's, he's been able to come up with this loop of key changes or chord progression, or I'm not exactly key changes at the very least, um, that Kind of sneakily can always, always, uh, increase.

jon_raw: 9:38

Yes. The infinitely modulating fugue. Uh, which is just a cool, cool name for something. There's actually like a modern example of this that I was reading about a long time ago. Uh, I think it was in Inception. You know how Inception has those crazy, like blah notes. Well, I guess, man, it was at Howard Zimmer or

geb_matt_ch1_p1: 10:02

Hans, Hans Zimmer,

jon_raw: 10:03

Hans Zimmer. Yeah. I'm thinking of like Howard's in or something. Um, Hans Zimmer. He. It, uh, use this technique where like, you're basically playing, uh, a note. It, it sounds like a single note, but it's like a lot of different tones and certain parts of the tone are going upwards and certain parts of the tone start lower, but like come up to the tone. And he's like changing the volume of those things where you basically have this tone that like, it sounds like the same note. Like the longer you play it, but it also sounds like it's going up. So it gives you this like extremely tense feeling. And that's kind of, that's one of the tools he used to create the soundtrack for Inception, which is an awesome soundtrack where it just kind of keeps you on your toes. It's almost like this. It's almost like he's tapping into your brain and like, I don't know, touching certain neurons to make you feel tense.

geb_matt_ch1_p1: 11:00

It's a whole, whole point of the movie. Yeah. I think, I think that's called like a, a shepherd tone. I like, there's like a, uh, rising shepherd tone and a falling shepherd tone. Um, yeah, just listen to it. It's, it's, uh, it's pretty surreal. Like, you don't know what is going on because it's hard to pin down. Like, you know, something like you can tell it's not actually getting higher, but you also can't, can't really pin down what is happening. Um,

jon_raw: 11:29

it's very uncanny valley ish. Like it kind of reminds me of, you know, the Spielberg zoom, like the Dolly zoom. I, Jaws is famous for having it where you're like, you know, you're physically moving the camera towards someone while you're zooming the camera out. So it gives you this really bizarre, like kind of perspective altering thing. It kind of reminds me of that where it's like your brain just doesn't really know how to interpret it. So it kind of gives you this like tense feeling.

geb_matt_ch1_p1: 11:58

Yeah. Yeah. Yeah, exactly. So that's kind of, I mean, that's what it all builds up to. I think ultimately, though, is this, this, um, this looping piece that Bach includes in his musical offering.

jon_raw: 12:14

Yes. Yeah. And my understanding is this is like very on, on topic or on theme for the book. Cause this whole book is going to be about systems that reference themselves and, constructions where you can take a construction and kind of like compute the next construction. But then it eventually wraps back. To itself. So this, this musical offering, it's almost like a, a real incarnation of this like extremely hyper philosophical concept. So I think what the author is trying to do is start the reader out in a place of like the real, like, Oh yes, I can interpret this. I can understand, you know, a piece of music modulating up keys till it eventually wraps around. Like that's kind of an, an. A more intuitive thing, but he's quickly going to dunk us into the deep end of the pool and start to get like very metaphysical.

geb_matt_ch1_p1: 13:08

But before he does, uh, he throws us another bone and he shows us the work of, of M. C. Escher. So that's the, that's the next, um, I don't know, icon. I would say almost in this book where, you know, obviously a very famous, uh, visual artist, um, with all of these like impossible structures where there's a building with staircases in, you know, In four directions that seem seemingly all lead upward in a way that like, would not actually physically be possible. Um, and then again, just immediately evoking, Hofstadter, that's the author. I don't know if we, we said it, but, um, Douglas Hofstadter evoking the imagery, uh, literally of, of the, you know, a strange loop.

jon_raw: 13:56

Yeah, exactly. So this is kind of another real world incarnation of this like strange loop concept he mentions. I like this phrase. He says Bach and Escher are playing the same theme in different keys, art and music. It's like they're, they're kind of manifesting the theme of this book. So I think that's. Like, obviously we haven't read the book. We've only read the first chapter, but it seems like this is why Bach and Escher were chosen is they sort of within their body of work, they like exemplified this strange loop recursive, recursive structure. But yeah, I didn't write too many notes for Escher. Like, I feel like Escher is included, uh, because he's very visual and it's cool to like, see the visuals in the book and get this, like, you know, You know, immediate visceral reaction, but obviously we're not going to be able to show the visit, the visuals in our podcast. Um, but hopefully he goes deeper into usher and, you know, continues to describe his work in ways that we can relay to the listener.

geb_matt_ch1_p1: 14:55

yeah. Um, I think the most, the most interesting. Example that he calls out is the drawing hands by, uh, MC Escher. And that's the one where it's two hands that are both, you know, drawn in pencil and they're drawing each other. And so like, this is, you know, this is exactly like you're saying the, the, these visual representation of, uh, of the strange loop. Um,

jon_raw: 15:24

Yeah. He also mentions Penrose tiles at one point, which I am a huge fan. You know, Penrose tiles are, um, Basically components that tile infinitely or tessellate, you know, you can fill a grid with these components. They might be like, you know, obviously like a simple square would work that could tessellate an entire grid, but you can also have much more complex shapes that sort of like mesh together and fill a grid. And that was kind of what Penrose, worked on, or at least part of part of Penrose career. I don't know that much about Penrose.

geb_matt_ch1_p1: 16:00

Well, one of the very interesting things about the Penrose tiles is that it's not, it doesn't repeat. Uh, you know, which, which I, it's like, it's a very simple, you know, you can get something that's just a diamond, but you, when you, when you tile them together, like they all lay flat, um, and, and you see patterns, but it never, it's not periodic. Um, and there's a very interesting proof of this, which is that. I'm going to, I'm going to butcher this, but basically the ratio of like two of the features of the shape is like the golden ratio or something. It's, you know, it's, it's a, uh, transcendental number. And in order for the pattern to, like the pattern eventually has to like, represent that number. So in order for it to repeat, it would have to, uh, you know, represent the number, you know, that, that ratio. So it's kind of like a proof that it does not actually repeat because, you know, add it, add infinitum, it has to represent a transcendental number.

jon_raw: 17:10

So when you say it doesn't repeat, are you saying like, because I'm guessing like similar, you know, types of things happen, but are they like slightly angular, you know, slightly rotated, or something like that?

geb_matt_ch1_p1: 17:24

exactly. So it's like their rotations and, and yeah, you'll get repeating like clusters of tiles, but it's not like, it's not a periodic. Uh, you know, pattern of, of tiles.

jon_raw: 17:37

Yeah, so not like squares. It's like some shape that doesn't repeat. Yeah, it doesn't repeat. That's crazy. I don't know. I don't know if I knew that. It's kind of amazing.

geb_matt_ch1_p1: 17:46

Yeah, I, I should see if I can find the video where they talked about that, but, and, and I'm getting the details a little bit wrong, but it did, it did wind up that like, it was because in order for it to repeat, it needed to like express some ratio between two of the like aspects of this shape, um, which was, which was, transcendental,

jon_raw: 18:04

I love that. but yeah, so, you know, this chapter discussion of Bach and Escher and, and Gödel, Bach and Escher, like I've, I'm sort of repeating myself a little bit, but those are kind of the two real world examples of these themes. But with Gertl, uh, he is going to get, you know, a little bit more into the metaphysical and discuss kind of the ideas behind this like self reference and, recursion.

geb_matt_ch1_p1: 18:32

Yeah, and the kind of irreparable damage that girdle did to, Principia Mathematica.

jon_raw: 18:38

Oh yeah, no, he owned that, but I think we'll discuss that in our next episode.

geb_matt_ch1_p1: 18:43

I'll see you, see you then.

jon_raw: 18:44

See you then, Matt.