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Music and mathematics are two distinct fields of study that have their own theories and approaches. However, they can learn from each other and both are based on fundamental principles. Chess is an example of a game with multiple layers that can be explored for a lifetime. Music is an abstract art form requiring creativity, and certain techniques such as intervals can be used to create tension and release. Plagiarism should be avoided and one should strive to make their ideas their own in order to reach self-actualization.

The speaker explores the relationship between music and mathematics, encouraging debate and discussion on the foundational objects of Mathematics. They suggest that narratives behind these foundations are part of the foundations themselves, and use the example of topology to demonstrate this. Chess is also used to illustrate how learning the basic rules and concepts can lead to more sophisticated conversations. Depth is defined as something that gives one mileage and has many layers, and is not just a vague term used to describe something that is profound or interesting.

Chess is an example of a game with a deep concept that can be explored for a lifetime. Basic concepts such as controlling the center and developing pieces are essential to understand, while intermediate principles such as tournament openings, critical pawn structures and planning development are used to deepen the understanding. Advanced concepts such as forks, skewers, pins and tempos, transitions and sacrifices are then used to further explore the game. Depth refers to how much an idea can be explored and developed, and there may be an infinite number of deep mathematical concepts.

Chess is a game that is simple to learn but difficult to master, while mathematics is easy to become familiar with but can take a lifetime to master. Chess may be deep, but it is not always seen as meaningful. People dedicate their lives to different activities and may not understand why others have made that decision. This is likely due to self-actualization, as people connect with certain things and find meaning in them. Rather than trying to find one's true artistic self or musical personality, one should try to find self-actualization in whatever one does and harvest a meaningful life out of it, regardless of its significance.

Philosophy can be divided into two categories - applied and pure. Applied philosophy involves exploring questions such as what is love, while pure philosophy is more abstract. Creating music requires both generative and discriminative processes, where the good kind of discrimination is when something feels inherently right with respect to the true self, rather than having an opinion on what the music should sound like. Writing music can be seen as an applied philosophical process, as it allows one to explore their true musical self, and it is important to not be opinionated when writing music, as this can lead to external influences being put into the music.

Creativity in music and mathematics requires embracing one's own personality and letting go of pre-conceived expectations. This is the biggest hurdle to creating something unique. To overcome this, one must generate a routine and an artistic habit, and inch away from the expectation of creating something massive. Mathematics can also be explored by engaging with constraints and settings to see the outcome. This can all help make the creation unique and inspiring.

Music is an abstract art form requiring creativity and thought to come up with good ideas. Musical techniques such as melodies and intervals are helpful tools for creating music. During the common practice period, music theory was developed by classical composers and later studied by academics. Intervals are categorized into consonant, dissonant and context dependent. Music is capable of creating tension and release through the use of consonance and dissonance by setting up different chords or melodies. The Pythagorean argument states that the ratio of a note's wavelength to the same note's wavelength up an octave is 1:2, however this may not be universal.

Music and mathematics are two distinct fields of study, each with its own theories and approaches. Mathematics has a more unified consensus on what is deep and beautiful, although this wasn't always the case. Both disciplines are based on fundamental principles and have ways of discovering the other. It is uncertain whether mathematics is universal, but it is possible to view schools of music as following from foundations in a similar way to mathematics, and music can even be used as an internal language.

Music is an important part of self-expression and creativity. Jimi Hendrix's cover of Bob Dylan's "All Along the Watchtower" is an example of creativity and exploration. Plagiarism should be avoided and one should strive to make their ideas their own. Basho's haiku captures the motivation for original work, while some classical music schools focus on preservation. Music should be explored and experimented with to make it one's own, as it is an important part of self-actualization.

Music and Mathematics have been a big part of self-actualization for many people, and the speaker is presenting their own personal philosophies on the two. They invite discussion and debate on the foundational objects of Mathematics. Canonical answers include sets, types and terms, and objects, but all have their shortcomings. The speaker encourages the audience to challenge and provide their own ideas.

Foundations of mathematics such as sets, proofs and syntax are difficult to understand without a narrative to follow. It is not a widely accepted opinion that the narratives behind these foundations are part of the foundations themselves. An example of this is topology, which is often taught with just the axioms, but deep consideration of space and continuity lead to the axioms. If the narrative is stripped away, it can be difficult to understand the concepts. Therefore, the narratives behind the foundations are in fact part of the foundations themselves.

Chess is a deep game. It has many layers and the more advanced concepts one learns, the more sophisticated conversations can be had. To demonstrate this, one must first learn the basic rules and concepts. Mathematics and music can also be deep in the same way. Depth can be defined as something that gives one mileage and has many layers. It is not just a vague term used to describe something that is profound or interesting.

Chess is a game which has a layer of complexity that can be explored for a lifetime. Basic concepts such as controlling the center and developing pieces on the back rank are essential to understand. Intermediate principles such as tournament openings, critical pawn structures and planning development are then used to understand the game further. Advanced concepts such as forks, skewers, pins and tempos, transitions and sacrifices are then used to deepen the understanding of the game. As more is learnt, it becomes easier to make decisions and improve as a chess player. This example of depth is what mathematicians become obsessed with and it is an infinite tower of knowledge.

Depth is a concept that refers to how much an idea can be explored and developed. It is different from breadth, which refers to how much an idea is connected to things outside of itself. Chess is an example of a game that has a deep concept, but there is an infinite number of other games which could also be explored deeply. It is uncertain whether there is a finite or infinite number of deep mathematical concepts, but there are some which are not deep.

Chess is a game that is simple to learn but difficult to master, and is often seen as poetic due to its simple rules. However, it does not correspond to anything in the outside world. Mathematics, on the other hand, is easy to become familiar with, but can take a lifetime to master. It also connects to many other things in the world, providing a web of meaning. Chess may be deep, but it is not always seen as meaningful. People dedicate their lives to different activities and may not understand why others have made that decision. This is likely due to self-actualization, as people connect with certain things and find meaning in them.

Finding one's true self is not only philosophically problematic, but practically as well. Trying to find one's true artistic self or musical personality can lead to an existential black hole, as one may think that is what philosophers are encouraging. However, it is unlikely that any serious philosopher would actually encourage this approach. One should instead try to find self-actualization in whatever one does and harvest a meaningful life out of it, regardless of its significance.

Philosophy can be divided into two categories - applied and pure. Applied philosophy involves thinking about questions such as what is love, and how it can help to shape one's behaviour. Pure philosophy is more abstract. Writing music can be seen as an applied philosophical process, as it allows one to explore their true musical self. It is important to not be opinionated when writing music, as this can lead to external influences being put into the music. Everyone should strive to not be opinionated about the type of music that is being created, as this can lead to more meaningful art.

Creating music requires both generative and discriminative processes. The good kind of discrimination is when something feels inherently right with respect to the true self, rather than having an opinion on what the music should sound like. For example, when someone else solves a problem in mathematics, it doesn't feel like it came from the person, but it feels right. This same sensation of "should" applies to music - deciding a priori what the song is meant to be and then creating it. This could be something like a black metal song, a pop song or something for an action movie.

The speaker discusses how striving for a certain style or image of music or mathematics can be a huge block to creativity. They suggest that this is due to the pressure to be unique and groundbreaking, and that this pressure is often a result of our own insecurities. To overcome this, the speaker suggests embracing our own musical or mathematical personality and letting go of pre-conceived expectations. This is argued to be the biggest hurdle to creating music or mathematics.

Creativity takes time, and no idea comes from a vacuum. To make something unique, one needs to generate a routine and an artistic habit, and inch away from the expectation of creating something massive. Mathematics and music can be inspiring, but one must detach themselves from the idea of their creation coming from a vacuum. Engaging with ideas authentically and bringing a sense of personality to it, can help make the creation unique. Mathematics can also be fun, by exploring constraints and settings, to see what the outcome would be.

Music is an abstract art form and requires creativity, personality, and thought in order to come up with good ideas. Musical techniques are helpful tools for creating music and include melodies and intervals. A melody is two notes played at the same time and a chord is three or more. Intervals are pairs of notes and can be listed since instruments like the piano have a discrete set of notes.

Music theory during the common practice period was developed by classical composers such as Bach, Mozart, Beethoven and others, and later studied by academics. Intervals in music theory are categorized into three groups: consonant, dissonant and context dependent. Consonant intervals are pleasant sounding, dissonant intervals are harsh and unpleasant, and the only context dependent interval is the perfect fourth. Pythagoras believed that dissonant intervals had a mathematical ratio between their wavelengths which caused a harsh sound.

Music is capable of creating tension and release through the use of consonance and dissonance. This is done by setting up different chords that harmonize the melody, or by placing certain flows of melodies that make the fourth sound either pretty or ugly. The concept of time is important when creating music and the Pythagorean argument states that the ratio of a note's wavelength to the same note's wavelength up an octave is 1:2. It is uncertain whether this argument is universal, as different cultures have different musical instruments and styles.

Music and mathematics are two different fields of study that have different theories and approaches. Music has different schools of thought such as common practice and jazz, while mathematics has different branches such as algebraic topology and algebraic geometry. The speaker suggests looking for principles that span across the different fields of mathematics. In contrast to music, mathematics has a more unified consensus on what is considered deep and beautiful. This was not always the case, as in the past different cultures had different opinions on the fundamentals of mathematics.

Mathematics and music are both based on fundamental principles and have ways of discovering the other. However, it is uncertain whether mathematics is universal, as an alien life form would have to set up a context and foundation to understand it. Music is similar in that it follows from foundations and complex, unexpected phenomena can emerge. It is possible to view the schools of music as following from foundations in a similar way to mathematics, and music can even be used as an internal language.

Music can be linked to various areas of mathematics through its language. To avoid self-betrayal, individuals should be aware of the potential risks of joining subcultures. Applied philosophy of music can also lead to self-betrayal if one gets too influenced by a particular subculture. Creativity and exploration are important aspects of music and should not be overlooked.

Music is an important part of self-actualization, and creativity and exploration are essential to it. Jimi Hendrix's cover of Bob Dylan's "All Along the Watchtower" is an example of this creativity. It is okay to copy, but it is important to play around with the idea and experiment with it until it is your own. Jimi Hendrix saw something inside Bob Dylan's song that Dylan didn't see and was able to make it his own. Music is a powerful tool for self-expression and creativity.

Creativity and originality are important aspects of mathematics and other art forms. Plagiarism should be avoided and one should strive to make the idea their own. Basho's haiku captures the motivation for original work, providing a sense of immortality. However, some classical music schools focus on preservation, where students must accurately reproduce pieces as Beethoven would have played them. While some find value in this, others cannot understand why someone would pour hours into reproducing something that already exists.

storytelling in music and Mathematics this is going to consist of a lot of personal opinions I invite anybody to pipe up to challenge things that I say to bluntly disagree with me to shout when you do agree with me to provide your own two cents I would be very interested in providing a bit of a back and forth between the audience and the speaker because these are things that I'm I'm going to be speaking today about some things that I've thought about a lot which come down to my personal philosophies on what music is on what mathematics is uh For Me music and Mathematics have been a big part of my journey of self-actualization which I think makes them very personal to me and I'm going to be presenting with that personal side of of both of these two things now what that means is that this isn't formal philosophy this isn't spoken about very heavily this hasn't been filtered through various different academics but I believe that these are in incredibly relevant parts of these two Pursuits and I think that every mathematician and every musician goes through some kind of development of their own theory of knowledge or their own theory of art or their own theory of mathematics and theory of music and I'm going to be talking very boldly about my personal ones um but I want to I want to say that in a way that invites discussion okay so don't look after me in today's talk let's let's let's discuss some of these ideas I'd really enjoy that what are the foundational objects of mathematics let's start with an amazing question right in fact I would argue that this question is not as fruit Barren as one would hope uh nor expect there are a few canonical answers but they all have their uh shortcomings and the fact that there are several of them I think is in and of itself a little bit peculiar once you're a bit more of an advanced thinker about mathematical objects and mathematical foundations it becomes clear that indeed there must be various different options for foundations but when you're a novice coming into mathematics I think it's very natural to think are there there ought to be one classical Foundation there should be one logic of the universe and that's the logic that mathematician study and so we do have if you canonical answers uh but all of these are a little bit a little bit perplexing so let's write down some canonical answers you might say that sets uh that which is foundational you might say types and terms of that which is foundational you could also say objects

you could also say points and lines or maybe geometry more broadly proofs man proofs you can say proofs very popular answer and uh you could say what's another example something like something like syntax right and and some of them stop learning together so the claim that I want to make is all of these foundations all of these suggestions they're incredibly difficult to understand unless you have some kind of a narrative that follows alongside them so if I were to take sets for example a set is very like if you go through the axioms obviously I'd have seen set theory right there's a bunch of them you can you can Google zfc set theory and you'll find um the Wikipedia page that uh details all of the axioms and if you just read these raw things they're incredibly difficult to pass and what Wikipedia does and what any any reasonable person that was explaining these ax seems to you would do is they will give you the formal definition and then they'll give you a description of what this is really saying right and it's this it's this phrase of what it's really saying that I want to dig into you today and so to put the claim to put the claim boldly in writing I'm going to say uh the the narratives Behind These foundations are in fact part of the foundations themselves and first let me argue that this is not a widely spread opinion uh the reason why I think this is not a widely spread opinion is because the way that it's because you couldn't just remove the narrative right and some mathematical Educators do this and it can be very difficult to understand what's going on when they when they do this I think a classic example is a topology class so in topology you learned that a topological space consists of a set along with a set of subsets of that set and that set of substances to satisfy three axioms you have to have the empty set inside that cell you have to have the whole set inside that set etc etc and it's very common that topology is taught in this way when you say here are the axioms and then off we go we then start studying topological spaces however it's clear once you start studying topology seriously that these axioms didn't just arise from nowhere they came from Deep considerations about what is space what is continuity in what what is the most general setting possible in within which we can talk reasonably about coaching sequences or uh function approximation etc etc and eventually you arise you arrive at these axioms and if you only just strip it away then you get a really good example

of what it looks like to just not have the The Narrative be part of the part of the foundation and I think that that's a mistake I think that indeed we should be accepting the narrative as part of the foundations itself and this is one of the main uh things that I think that mathematics has to learn from music so I'll be coming back to this point later in the tour first I want to talk about depth and by depth what I mean is um this vague term that people use when they're very passionate right so oh this this piece of mathematics it's very deep and you should pay attention to it obvious there's other results I think ultimately that's shallow and it's not it's not really going to lead to something so let's see if we can tie down some kind of concrete definition of what we mean by depth and then we can use this in order to explain how music is deep in the same way that mathematics is deep so the question is what does it mean for something to be deep now I've arrived at an opinion of this because this was a phrase that always kind of confused me a lot I heard a lot of mathematicians talk about how this was deep and that wasn't deep Etc and I always kind of thought that what they meant was this is significance or this is profound or this is quite interesting or cool like this is really cool or something and I never and I never knew really what they were getting at but as I paid more and more attention to the things that they were calling deep and the way that they would describe the death I found that there was quite a similar way that mathematicians used the word deep and what they mean is they mean deep right so there are there are many many different layers to it and you can kind of keep further going down and the more advanced concepts that you learn the more you can have sophisticated conversations about this thing in a way that continues to give you mileage so I think there's a very simple uh like demonstrative example of what uh of what something of what it means for something to be deep and we'll start with that example and then and then we'll see if we can get some kind of concrete definition down so I said that I was going to talk about mathematics and music but I'm going to start off by talking about Chess so literally the board game cheers so I'm going to assert that this is a deep game and the reason why is because first one must learn the basic rules and the basic concepts right so let's forget the basic rules because everything has got basic rules so there's always a zeroth

step but the first step would be the basic concepts basic concepts uh so develop uh pieces quickly and by pieces I mean your um pieces on the back rank right so don't don't spend too much time at the start of the game moving your pawns around uh control the center uh develop notes towards the center Etc right so there's a kind of Elementary guiding principles for the gaming chess now that's pretty cool but what's more interesting about Chess is the fact that once you have understood these Concepts they then Grant you the language and the understanding of the game to allow you to then learn the second layer of the game which is a higher level of complexity right and a higher level of sophistication uh with that talk towards the decisions that you're making in the in the moves okay so there are some intermediate principles I can't spell this morning intermediate principles so there's a yeah okay basic concepts intermediate principles uh so so tournament openings or like book starts they call them not a very a lot of very good chess player by the way uh critical horn structures okay and then uh planning select development I feel like it would be nice if I had a better uh example here maybe if I go into advanced concepts so Forks skewers pins and you can see we're developing terminology now so hopefully this is stuff that you're not really aware of because the point is in all that you describe any one of these I need to use the language of the previous layers right tempos transitions sacrifice Etc and then it just keeps going right so highly advanced and I can't say anything about that and what is interesting about the gaming chess is that you can spend your entire life learning it and still learn more right and that's what we mean by deep and and also it's not just that you can spend your whole life learning uh learning it and still learn more it's more than that it's that you can spend your whole life learning it and you can still learn more things that will that will genuinely make you a better chess player right so it's same it seems as though there is this infinite Tower above uh the game of chess where every next layer depends on the layers before it and as you get further up you genuinely are still learning relevant material in order to deepen your uh understanding of the game right so this really gives you a concrete example of what we mean by depth and I think that this is what mathematicians get kind of obsessed with so when there are because because there are such thing as quite

shallow Concepts inside mathematics you kind of get to a point where it's like okay this seems to be most that you can say about this idea this idea is fully explored and we're kind of at the end of it so that's a relatively shallow uh concept versus something which is uh deeper which just goes further and further and further in development the more that you build uh terminology and language toward it okay does anybody have any comments on my uh observation of of what depth means yeah I feel like I would I guess I agree with everything you said on this board but I wonder how much it depends on my sense that chess is not an arbitrary point in the space of games I mean if you tell me that there are infinitely many games you know not slight trivial variations on chess but you know their own thing which have a similar structure from simple Concepts to medium Concepts and advanced uh and I could choose one from this billion possible games to develop my understanding of and spend my life mastering if you told me there was an infinite supply of such things that might suddenly feel that any given one was kind of pointless and just a bit of a an illusion uh kind of to put it bluntly masturbatory kind of activity right where you're just sort of it's just it's not really connecting to anything outside of yourself right if you're just engaged in following this one arbitrary game to its conclusion um do you think that changes your sense of depth so that depth is not really an intrinsic thing to the game itself it's something about the the like the rest of the possible games I don't know yeah so what is kind of missing for my definition here is uh the the the relevance to things outside of the thing right but the problem is that's that's kind of breadth at that point so I'm not sure if that's really depth but Brett is also an important Concept in whether something is significant and this is where where concepts of profundity Etc do do become um blurred with depth a little bit so first and foremost I mean you've you've asked a complex question um I would respond with do you believe that that's not true I mean even of mathematical Concepts do you believe that there are infinitely many deep mathematical Concepts or do you think that that's finite people I don't know I don't know either right and also even if it's infinite I don't think that's as significant as the fact that there are some that aren't so even if chess is one in an infinite number of deep games there are at least games that aren't

deep like Go Fish what are you gonna do what are you going to do with that game right so maybe you can learn some psychological techniques but I don't think it's got the same depth uh as as a game like chess uh I also think that for chess specifically people get a bit um what's the word poetic about it because the rules are so simple to describe right which is also not really true because no one really knows the full rules of Chess because there are heaps of them and they're very complicated and there are lots of any cases and cases to consider but in but like it's it's approximately accurate to say that because that chess is simple to learn and difficult to master and there are mathematical Concepts like that as well for example the prime numbers very easy to become familiar with and to write down and to understand and to learn some basic theorems about but you could literally spend your entire life learning about them chess is somehow doesn't correspond very closely to anything in the outside world knowing just doesn't let you predict you know Spectra of stars or something right but plenty of mathematics seems to correlate with many other things out there in the world so I feel like when you say a mathematical fact is deep you don't necessarily care that it connects to anything in physics or anything so mundane is that if you're a mathematician but there's it's kind of like this web of meaning to which it connects from which it draws its depth so I I'm really not sure I think chess is deep I think like you can entertain yourself with it and it's not easy but yeah I I guess I I have a feeling that like Chase is maybe deep or away she is deep but I I guess I struggle a bit with looking over the fan set the way cheap players like Lisa doll and being like ah you fool you spent your whole life doing this pointless activity and then I'm like shut up don't say the same thing about me so well I think that again just to repeat my first answer I think there's a question of depth verse breath here so let's put that on the board and secondly I think the I think the main reason why people who have dedicated their lives to particular things and look over at other people that have dedicated their lives to other things and they don't understand why they've made that decision you should be doing this or I just would not feel that way if I if I were doing what you were doing I think it comes down to self-actualization I think that people uh connect with certain things and they

harvest a um meaning of life from it and that's going to be the thing that you end up doing now whether that is a thing that actually is genuinely deep or actually is genuinely broad or is Meaningful or insignificant or isn't significant whatever it's kind of outside the question of whether you're going to spend your life doing it right like you're gonna like whether it means it's deep or not you're still going to do it if you find self-actualization inside it I think that's the observation that I've made so people find self-actualization in Sanchez people find self-actualization inside speed running uh crappy Nest game that was made 25 years ago 30 years ago it there's a question of whether you're going to um get reflection of self from it so whether you're going to harvest an artistic experience from it and that's kind of external as to whether the theme itself is actually deep so I think it's reasonable that my definition seems a little flat right it's kind of like oh well I don't I think that my deep thing is way deeper than just for anything that satisfies the implied definition of what we have here I think that's reasonable but this at least puts something on there um on the table and and also I'm going to I'm going to transition now I'm going to transition into my next point because one thing that I want to say uh okay there's a clever way that I could turn this all together if I can get my brain to function um recall that last time oh my God I just lost my point sorry give me one minute um while you're thinking I'll insert the comment well said about you okay um oh yeah there was this whole thing about stop trying to find your true self okay I remember my point good okay so last time um there was a criticism criticism which was stop trying to find your true self because this is philosophically problematic it's not really philosophically problematic but it's practically very problematic right you might end up not doing anything because you don't think that this is really the truest version of you and you might fall into a self-existential black hole where you're trying to find yourself inside the abstract and you might misunderstand previous philosophers to think that's what they were encouraging you to do where it's very unlikely that any serious philosopher was really encouraging this and I understand that criticism this criticism came up because I was talking about trying to find your true artistic self and and your musical personality when you're trying to

develop music but I want to draw a distinction here between well one side of the coin is I'm going to say applied philosophy and the other one I don't know what it is but it's not applied philosophy other so pure philosophy or something like that this is kind of where the problem lurks is inside other so you could become confused and you can think okay philosophy is in general a good thing I should develop a more and more abstract concept of self and I should really think think think about that until I make any important decision because otherwise I run the risk of making the decision that's not aligned with my true self and then I and then I end up with regret and the waste of life okay that is kind of where the problem is by applied philosophy what I mean is there are some philosophical questions that are really helpful to think about because they will genuinely make a difference to the way that you live your life and it will make you live a more practical life and it will make you live a you know a good life and a better life and all of these other vague terms it can philosophize about so for example a question like what is love what does it mean to fall in love uh it's a very applied philosophical question because as you think about that and as you philosophize about that more the way that you interact with love is genuinely going to change there will be visible difference in the the way that you present yourself like who you present yourself to etc etc so so that can be a very helpful thing to think about as long as it's rooted in a concrete tangential change in your behavior right and that is where I want to put like find your true musical self with the application of writing music right uh so here it's foreign musical self so that you can write music and I think it's very likely that if you were to do this you'll start harvesting self-actualization from it and that can become a very deep and philosophical experience for you and that generates art and music is Art so that's a good thing if that were to happen if that were then not happen then at the very least you're not going to put your external influences into your creation of music so the point that I'm trying to make here is you want to not be opinionated about the type of music that is coming out of you and if that seems weird it's not this is so much so much so it's so everywhere that I can't even tell you it's one of these things that people don't realize they're doing and everyone thinks that everybody else is doing it

but they're not really doing it and when you become more in tune with it you can start removing those uh like okay so let's put it like this let's put something like this well okay I guess I guess the real no no let's put it like this don't have an opinion on what the music should sound like during its creation [Music] I think I kind of know what you mean but obviously you're alternating between generative and discriminative processes in music like in math and the discriminative process has to be something like what you think it should sound like but so could you I think you're discriminate you're distinguishing between two kinds of discrimination and could you maybe put your finger on what the good kind is the the good kind is the one that it doesn't seem like you did it right and this is what I'm trying to do no sorry I was just agreeing and and and that's what I'm trying to trying to nail down here and and yeah you're right it is confusing the way that I'm writing it so you could say should as in like when so picture when somebody else solves it for you so maybe this is easier to explain in mathematics so you're sitting down and you're thinking thinking thinking you're stuck stuck stuck in your client working out and you've been like you've been in that state for a month and then imagine somebody else comes along and they say ah uh yeah have you thought about doing it like this or have you heard of this paper have you heard of this technique and they write something on the board and they and they write down like what is just so obviously the answer to the question right and you're looking at it and you're like yes yes yes that that's it that's it that's it that doesn't feel like it came from you because somebody else came into the room and they wrote it down and you had that experience of it was not you that did that but it feels so right in a way and that's the sense of should wear it where it should that's the correct version of should so that sensation of this is inherently right with respect to my uh like the the phrase I want to use is true self so with respect to the the universe this is the correct idea to go here or you could be saying to yourself I want to write a black metal song or I want to write a top 40s pop here or I want to write something that could be used in an action movie right so you're kind of deciding a priori what the song is meant to be and then when you start trying to create it you might be thinking oh no this sounds like Soul

Funk or this sounds like a jazz song or something and you're like no no no that's that's not right that's not right that's not right and then you start bludgeoning it so there you're really forcing it to be a particular thing and it's like why right and I think that there are normally toxic reasons why we are wanting our theorems or our music to be of a particular style or to look a particular way and I think that that gets in the way and I think it gets in the way hugely so I'm trying to help people understand that this is a block this is a blockage that arises from writing music and in fact it's a main one it's much more of a block than the other blocks that you think like oh I can't play guitar or I don't have the right software and stuff like this no no no no no it's just not as big of a like that's not the hurdle you can always make music with what you have like like always right and what's actually going to stop you from running the music is the the self-struggle of oh this is not the type of music that I want to make it's meant to sound like this I wanted to do this I'm inspired by these people I want it to be like that and I think that that blurs your musical personality and I think that the uh Journey that you're going through as a musician of ridding yourself of those pre um expectations of what the music should be and also how how it should reflect on you is the biggest hurdle in music writing and I think it's the biggest hurdle in mathematics creation as well right I mean you've seen people you see people want to become mathematicians because it makes them look smart and stuff and they don't realize that that's why they're doing it or it looks like success or they've got some kind of personality that they're attributed to it and they don't even realize that that is their biggest hurdle towards good mathematics right I just think the exact same thing exists inside music and I don't think I've nailed it here but how do you distinguish that from the kind of pathological desire to do something really new man uh which is just debilitating and it leaves somebody just wandering off into trivialities I mean yeah yeah that's a really good question I think it's just another example of the exact same concept right so if you've because you've decided a priori what it's going to be before you've even started right like before you even have any idea what the idea is you're saying it has to represent uniqueness and Novelty and it has to be groundbreaking so I see it as like kind of bad parenting

that's the analogy I always like to use like if you haven't even met you in child yet they're still in the womb and you're like oh they're going to be the world's best ballet dancing just like I wanted to be but couldn't on that fateful day when I'm profiling whatever I'm making a joke but you get what I mean you you need to be familiar with the thing before you have any idea what it is whatsoever and you need to generate that feedback from Loop between you and yes and there are many different ways that you can do that and mathematicians saying oh man I need to make this breakthrough thing I really wanted to be unique I want it to be massive at the same time I don't think that's a bad um motivation you could be inspired by mathematics because that has happened before and that part of mathematics is very beautiful and that happens in music as well like there are some albums that people release that honestly feel like they came from a vacuum and you're just like how did they think of this right and it's so amazing when that comes out and that could be very inspiring so it's good to be inspired in that way but deciding that your creation has to be that before you even started on it is so disabling right it's going to make him very difficult for you to um to either do that like it's kind of the worst possible way to to do that if you really want to make something unique and novel you have to generate like a routine and an artistic habit and you inch away there and it won't seem like it came from from a vacuum to you it just might seem like it came from a vacuum to other people and so you have to go through that Journey you have to at some point find a way to detach yourself from that personality and from that expectation and from that home and I think that philosophy is the way that you do that you come to understand that you're part of a bigger thing that uh creativity takes time and other people's ideas influence yours nobody does exist in a vacuum and no idea does come from a vacuum and the more that you engage with them authentically the more that you can bring an aspect of Personality into it right and that's really helpful it's helpful in mathematics as well when when people are discussing ideas you can bring your personality to it and you can almost have fun with it you can say oh wouldn't it be like funny if this turned out to be true or one of the be cool if we did it but like with this constraint or what if we did it in this other setting I wonder what that would look

like and they're actually good ideas that's what having a good idea really looks like and I think that having a a personality like I don't know how to say it if you're a mathematician you need to have a mathematical personality if your musician needs to have a music personality if you're an artist you need to have an aesthetic personality Etc I think having that personality and being playful with it and and passionate toward it is the best way that you do end up having these good ideas and it requires major steps of thought and self-actualization and self-realization in order to get there and so I think that these philosophical ponderings are in genuine part of um of of significant creativity when you're dealing with an abstract a sufficiently abstract artwork and Mathematics and music are both incredibly abstract and if you don't think music is abstract then like just think about the concept of crying do the music like that that's crazy right that's what what's happening there so it's definitely abstract okay any more comments on that before I go into another concrete point [Music] nope thanks so a kind of dumped a lot of my my content Out of Water there so okay let's let's do something a bit more concrete now that's a good idea so uh oh yeah oh yeah I remember now so the point that I wanted to make was uh we have this concept of depth I want to argue that music is also deep in this way uh and that's that links to one approach to music it's a very helpful approach to music because it will give you some basic tools that you can use in order to really start creating something and these are called musical techniques so I spoke a bit about music techniques last time but you can talk about these infinitely so I'll give a few more now and it's important to understand that rules are made to be broken Okay so let's talk about Melody and I'm going to actually teach in something now okay so let's look at a piano um I used to draw these things all the time one two three four five six seven eight I think that's all I need good okay that's an octave of a piano okay and we have the concept of an interval which is just a pair of notes so three notes played at the same time or more that's going to be a chord a single note is just a note and then two notes played at the same time is is an interval okay and we can list the intervals because we've got a discrete set of notes here right if I wanted to choose a different instrument like a violin that has a Continuum then we wouldn't have been

have a finite number but for the piano we do have a finite number of intervals uh there were 13 of them these are unordered intervals okay and okay so what I want to say is in CL in in music theory we categorize these into three different groups but what do I mean by in music theory in music theory are literally mean during the common practice period the common practice period was Bach Mozart Beethoven list shop and you know all of the all of the famous classical composers and this was an important moment in history because uh complex musical techniques are being developed by these artists and not in any written way so it was later that uh that academics went back and studied their musical scores and then extracted these musical techniques from those people um but it's called the common practice period because lots of different musicians were doing the same thing at the same time although fun fact classical music theory is is based almost entirely off bark specifically so this is really to be taken with a grain of salt we're basically talking about one person's musical Like rules but it gives me a really good starting point and ultimately we want to develop Howard so let's organize these into consonants which is point on quite Pleasant sounding dissonant which is ugly sounding and then context dependent okay and the first most basic interval if I were to start with issues in the arbitrary note here this is the note C but it but it doesn't matter if I were to take the two notes C and C okay so I'm just taking the same note twice then that's called a Unison and that's considered consonant okay if I were to take C and the neighboring note that's a C sharp this gives you a terrible mathematical ratio between the wavelengths of these two notes and it was Pythagoras who believed that that like led to a dissonant sound and it does sound very sharp and very harsh they use this in like dramatic moments in horror movies and like intense moments of classical music Etc so that's a minor second and that's dissonant cool and then the major second is the next one up and this is also considered uh dissonant and I think you'll agree if you heard it so this is a major second and then Etc right so there are lots of uh consonant intervals and lots of distance intervals and the context dependent one there's only one and it's uh the perfect fourth so in the current context that would be C with an F and a love I love the fact that one of them is context dependent right because I think that's just an offering of

infinite creativity it's like immediately and you're sit with this exercise write a piece that uses a perfect fourth in a setting where it is sound as cons it's oh my God my words word sounds consonant and then I run another piece where a perfect fourth sounds dissident and you can do that by setting up different choices of chords that harmonize the melody or by just putting certain flows of Melodies around it that make it kind of make the melody land on the fourth in an ugly way or land on the fourth in a pretty way and it's it's really really it's really cool that music does this because it looks so limited like I mean you just have these notes sitting there and you've only got 13 intervals it's like what are you going to do but then the context dependency tells you what you're going to do you're going to have to take the concept of time seriously Etc I just think that's it's really cool that one of them is a is a context it's considered context dependent okay and we want to use consonants and dissonance uh as tension and release but I said that the wrong way around so consonants use that as release and dissonance use that as tension okay so let's think about this as release and tension so I've had this conversation with Lucas before we how much of this is just we're trained to recognize this and how much is like somebody who just encountered western music for the first time would totally get this correlation yeah that's a really good question the only way that's enlightened the only real argument you can make that this is somewhat Universal is that Pythagorean argument so have you seen have you seen this before it's like a um the ratio of a of the wavelength of a note and then the wavelength of the same note up and octave is literally a one to two ratio so you get this nice fraction one half right and then I think that a perfect fifth is a third or something and then I think a major third is of fifth maybe I don't know what they are but you get all the nice fractions of all of the consonant ones right yeah and then a different one I'm too ignorant to know whether that I should buy that argument or not do you think that's the explanation it's a genuine question I'm not being scared about something yeah yeah I'm I'm not so sure to be honest the reason the reason why I'm not so sure is because you're completely correct that if you go to other cultures none of this exists not even the piano and obviously they're enjoying the music I mean you know you go to Africa right and some African

music is like purely uh acapella backed with percussion right and so there there's a lot of um chanting there's a lot of Rhythm and that is just a complete violation of everything that the common practice period tells you but obviously if you're raised in that culture and you're you're finding the music Pleasant you're not you're not thinking like oh damn I just love these top these dissonant tones over and over so they're obviously not thinking that so the way that I the way that I think about it and my grand my grand musical theory for once I've got time in my life is that we have different schools of uh musical Theory so you can write common practice and you can write like even Jazz for example I mean these exist in complete juxtaposition from each other and they're both Western right so it doesn't even merely depend on a culture right and then I don't know other cultural music Etc and so there's all kind of exist as theories inside the realm of music and what I've always what I've always wanted to do is to look at mathematics with all of the different fields of maths and ask if there are any princes that go across here right and the reason why I think that kind of answers your question is this is just one theory of Music where in a given context you know with a certain narrative it all makes sense and it's helpful to think about these notes in this way in this context for these pieces Etc but it's the same in mathematics you might want to think about space as an algebraic topologist and you might want to think about space as an algebraic genometer and they're completely different opinions on what space is but like the analogy with music is sort of okay well these two musical practices evolved separately and they have different opinions about basic questions um that isn't doesn't really seem to be true of mathematics right it's not that Chinese mathematics came up with like a different attitude to foundations it's not like this Chinese foundations and uh Arabic foundations and English foundations and they have different opinions about what is deep and what is beautiful I think people more or less agree in a way that seems maybe I'm wrong but it seems to be much more of a consensus than it is with music I don't know if you'd agree with that isn't it true that when the world was more separated that wasn't really how that wasn't really true like didn't think Chinese believe that the the numbers were fundamental and the Greeks believed that geometry was was

fundamental and they both had ways of discovering the other through their thing but they really had different gods in their in their foundational understanding of mathematics but also okay there's always this question of like is mathematics Universal if we found aliens would they have the same mathematics as us and the problem is I think that I think my answer to that is yes aliens would have the same mathematics as us but that's not significant that they would and the reason why is because you might talk to an alien and if you want to ask them oh oh do you do you also have the Raymond Rock theorem and then they say what's the Roman Rock theorem and then you kind of have to explain what the Roman Rock theorem is to them and when you're doing that you're you're setting up a context and a foundation so that you can then describe the room and rock them which is a consequence of of that foundation so an alien life form would be like oh yeah maybe we've found that or maybe we haven't found that or maybe our version looks slightly different but if you were the do it your way then yeah I can see that you would have to arrive at your version of the statement so mathematics is this like study of what follows and not what is so if we talk to an alien Foundation they'll agree with us that that is what follows from what we did right but that doesn't really mean anything about the universality of mathematics and I kind of see music in the same way it's like you've got these if you've got you've got reasons why these schools of thought have developed and there are relationships between them as well and you do get complex unexpected phenomena emerging I mean people have drawn some of these links right like these these do exist you might think that they're bad or you might think that they're uninteresting but some of them do exist and I think it's not crazy to view these schools of music as following from foundations in a way that could be similar to mathematics if you were to explore these red links maybe there are none but I think I would find that more surprising I would I would I would not be surprised if there are there is some kind of similar story between a field of mathematics and the field of Music where the immersions and the story that they tell has a non-trivial relationship between the two of them so for example one of the one of the best ideas I've heard for for this kind of thing just by talking to people is using music as an internal language right so there might

be some geometric setting or some category theoretic setting where one of these languages of music is sound with respect to that area of mathematics now there it doesn't have to be the the deepest link possible it's just what is stated inside this one language infers something on the other and maybe it's not complete or something but I would think that that's something right anyway that's like a famous like controversial type episode okay I've done about five minutes left so I want to again I prepared way more material than I ended up presenting but what I should do is give some responses to some of the things that were brought up last time because a lot of great discussion came up last time and I want to want to actually actually give some responses to them so okay stop trying to find your true self so I did I did talk about that already but I'm going to put something else on the board which I think is really important so for yourself what we want to do is avoid self-betrayal and this is important and I think that a concept like subconscious and sub-communities which again was brought up last time a very deep idea and they were very deep concept and they emerge from actually amongst communities so it's a very human thing it's normal but there are and it's a good thing and there's like good things about it but there are problems and I think the main problem that come that comes out of uh subcultures is self betrayal so like tattoos that people regret drugs that people regret taking and I don't know violence is also an example in certain subcultures um these are things that people do because they think it's going to make them fit in but it becomes self-betrayal because that's not who they really are to do those things and that's very very serious this is really important for an individual's life they have to tune into this in order to to reach self-pace some some element of it and you can really ruin that for your entire life anyway that's getting too serious but bringing back to the applied philosophy of music you can do the same thing you can just self-portray by getting too influenced by a sub culture right and there's just like further extends the point I was trying to make earlier okay let me finish my responses and then we can talk so uh music outside of uh creativity and exploration so yeah I was quite snobby towards uh people who are not training music like uh some self-actualization exploration like you know engineerative thing I've thought about this and I think all

I can reasonably do is is refrain from commenting right to me music is such a big part of my self-actualization and I would not have had that self-actualization if I wasn't uh approaching music with such a focus to creativity and Ingenuity and self-explanation exploration of music and things like that it's just so much so what music is to me that I don't know anything else right I'm not I don't I don't have any interesting thing to say I don't have any experience in in stuff outside of that but I have a lot of experience within this so I think at the end of the day all I can say is there are other sides of music I don't really know much about them right but in terms of creativity and exploration I do feel fit to talk about it and that's what I've tried to do I'm gonna draw a man with his mouth zipped close okay and then creativity in repetition so somebody uh posted uh what is it Jimi hendrix's cover is that right yeah Jimi hendrix's cover of All Along the Watchtower which was originally by Bob Dylan right now this is just not a fair um example of what I'm talking about when I'm talking about uh releasing the same music that has already been already been made so when I Was preparing for this talk I did go and find a pile of uh songs that have been released by different artists in different countries in different decades that I just think So within the same isomorphism group that basically equal to each other but it felt like a bit of a nasty exercise I didn't I didn't really want to get up here and like points to these songs and be like look at how uncreative they are so I found such things but I'm not going to present them but what I want you to understand is that Jimi Hendrix completely changed Bob Dylan's song and he made it his and there's of course creativity involved in that and you and he's making the idea his and it's that's just really not what I'm talking about when I mean releasing the same ideas so what I'm going to put here is it's okay to copy but play around with the idea and experiment with it for long enough until you can rightfully say that it's yours foreign that's what Jimi Hendrix did so he saw something inside Bob Dylan's song that that Bob Dylan didn't see right Bob Dylan saw what he saw in that song and Jimi Hendrix saw what he saw in that song and Jimmy Hendrix was presumably a fan and was like oh cool I'm going to learn this song and you know I'm gonna and as he's learning it as he's playing it he's becoming so into it that he's making it his own and I think that's

really honest and I think that's a really important part of um creativity and you can see that in mathematics as well like all PhD students write their own notes on things that have already been uh well understood for years and years and they've already had many different volumes written on them it's not a waste of time you're making it yours right and that's really important but there there is a difference it's hard to Define but you know it when you've done it right like if you're making it yours then that's a good thing you're finding a way to uh you know you're developing your understanding of your own personality with respect to this art form and that's necessary and important and good and you can even release that if it became sufficiently personalized but be aware of the difference between just plagiarism and making the idea your own and I think that this is a good start take out a copy but play with the idea for long enough until you can rightfully say that it's yours okay I'll conclude there and we can have some questions and discussion thanks will you're welcome okay we're there Christians in the chat that weren't AI odd in the AI one's not coming to that anymore uh the AO doesn't appear in the chat no I think most of that's talking to the Bots um I'll communicate one of the Haiku which was basho's Journey ends illness takes him from this world Haiku live on still which I think captures another major motivation for doing creative and original working right it's a kind of uh suppressed player immortality quite often um yeah I think you can go too far with that as well though do you know that a lot of the um conservatorium like the classical music schools that's so much of that is Preservation so you learn to play the piece the way that Beethoven would have played it right and the idea is that you lose marks if you kind of put your own personality into it and the the people that do best in those course are those that that reproduce What Beethoven did as as well as possible and I don't know maybe that's veering into this second thing like music outside of creativity slash exploration where I don't really feel fit to comments I personally just I can't see why somebody would want to pour those kinds of hours into music and then reproduce as accurately as possible something that already existed people obviously do that and Find meaning in it and value in it and governments fund it as well so it must be important for some reason but I think that you can I personally think you can go