COMPLEXITY: Physics of Life

Tyler Marghetis on Breakdowns & Breakthroughs: Critical Transitions in Jazz & Mathematics

Episode Notes

Whether in an ecosystem, an economy, a jazz ensemble, or a lone scholar thinking through a problem, critical transitions — breakdowns and breakthroughs — appear to follow universal patterns. Creative leaps that take place in how mathematicians “think out loud” with body, chalk, and board look much like changes in the movement through “music-space” traced by groups of improvisers. Society itself appears to have an “aha moment” when a meme goes viral or a new word emerges in the popular vocabulary. How do collectives at all scales — be they neurons, research groups, or a society at large — suddenly change shape…and what early warning signs portend a pending bolt of inspiration?

This week we talk to SFI Fellow Tyler Marghetis of UC Merced about regimes and ruptures across timescales — from the frustration and creativity of mathematicians and musicians to the bursts of innovation that appear to punctuate civilization and the biosphere alike.

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Related Reading & Listening:

“Creative leaps in musical ecosystems: early warning signals of critical transitions in professional jazz” by Matt Setzler, Tyler Marghetis, Minje Kim

“The complex system of mathematical creativity: Modularity, burstiness, and the network structure of how experts use inscriptions” by Tyler Marghetis, Kate Sampson, David Landy

“An Integrated Mess of Music Lovers in Science” – press release with video playlist of the 2020 Musicology & Complexity Working Group

“Explosive Proofs of Mathematical Truths” – Simon DeDeo SFI Seminar on inductive networks

Complexity 29: David Krakauer

Complexity 33: Tim Kohler & Marten Scheffer

Complexity 35, 36: Geoffrey West

Complexity 37: Laurence Gonzales

Complexity 65: Deborah Gordon

Topics Discussed:

• competitive wrestling to complex systems science
• free jazz ensembles as a mode of distributed cognition like ant colonies
• creative transitions as analogous to ecosystemic transitions (loss of resilience due to autocorrelation, etc)
• the difference between composed and improvised music
• creativity and boredom
• the relationship between improvisation and trauma, exploration and nonlinearity
• the death of the genre (?)
• the role of the body in thought
• how can you tell an “aha moment” is about to happen?
• what does a healthy mathematical ecosystem look like?
• burstiness and virality

Episode Transcription

Tyler Marghetis  (0s): In saying that jazz is like an ecosystem that foregrounds the bi-directional non-linear relations between different componentsand makes hazier other aspects of jazz. That might also be interesting. But in both cases, you have this really interesting nesting of timescale. I think you were hinting at that a bit with your discussion of mass extinctions, where one thing that a mass extinction does is it resets the accumulation of timescales. It resets that lamination of deep history, moderate history, recent history, and all of a sudden you get these generalists becauseyou don't have these wonderful arroyos that have been laid out by the long history of the ecosystem.

And you definitely do have that in jazz, even in free jazz. 

Tyler Marghetis  (51s): So yes, in freeJazz, they don't have a written out score that they're riffing on, but there is a long history of practice and norms that all of these players have internalized. You can't just get a bunch of random musicians together and be like play. There's a genre, there's a set of expectations. And those have a history. And what I think is really powerful about this ecological metaphor is it sheds light on those multiple timescales.

Michael Garfield (1m 39s): When in ecosystem and economy, a jazz ensemble, or a lone scholar, thinking through a problem, critical transitions, breakdowns and breakthroughs appear to follow universal patterns. Creative leaps that take place in how mathematicians think out loud with body chalk and board look much like changes in the movement through music space, traced by groups of improvisers. Society itselfappears to have an aha momentwhen a meme goes viral or a new word emerges in the popular vocabulary, how to collectives at all scales be they neurons research groups or a society at large suddenly changed shape. And what early warning signs portend a pending bolt of inspiration. Welcome to Complexity, the official podcast of the Santa Fe Institute. I'm your host, Michael Garfield, and every other week, we'll bring you with us for far ranging conversations with our worldwide network of rigorous researchers, developing new frameworks to explain the deepest mysteries of the universe.

This week, we talked to SFI fellow Tyler Marghetis of UC Merced about regimes and ruptures across timescales from the frustration and creativity of mathematicians and musicians to the bursts of innovation, that appear to punctuate civilization and the biosphere alike. Speaking of creative bursts and breakthroughs, please, excuse us for getting this episode out weeks later than scheduled. My second child came sooner than expected last month and our communications office has been busy dealing with knock on effects.

Michael Garfield (3m 17s): Ifyou value them research and communications efforts, please subscribe to Complexity podcast or wherever you prefer to listen, rate and reviewus @applepodcasts and/or consider making a donation at Give you can find numerous other ways to engage with us at Thank you for listening. Tyler, welcome to Complexity podcast. 

I think I've been chasing you for what, two years now or something like that. 

Tyler Marghetis  (3m 53s): Yeah. And Ihaven't been running away. It's felt more like a dance than the chase, so I'm very happy to behere.

Michael Garfield (3m 57s): Fair. Yes, actually, that's funny because you know, that's one of those Lakoff and Johnson metaphors we live by, you know, is love war. Is love a dance, the journey. It's a journey. So we're on a journey together. And I think, you know, consequently, this journey will be one in which I'm constantly exposing my own implicit cognitive biases just in the way that I speak and gesture through our conversation. 

And so for anyone who can't see, my hands are doing this and Tyler's hands are down here. All right. Well, anyway, the first one I want to talk with you about was a piece that you presented on briefly in last year's working group on complex structures in musicology that this piece on creative leaps in musical ecosystems, early warning signals of critical transitions and professional jazz, which honestly is kind of like a drinking bingo victory for me with like all of the possible, you know, like how did you manage to fit all of this interesting stuff into one, one paper?

This is a Matt Setzler and Minje Kim that you wrote this with. We need to loop back and give people a little bit of biographical stuff so that people can get a sense for who you are and how you became a complex systems researcher and ended up at SFI. And why it is that you're animated to study the kinds of things that you're studying here.

So yeah, a little bit of backstory, please. 

Tyler Marghetis  (5m 47s): It's been a circuitous route. I was not an early acolyte, although
maybe sort of an early fan boy of complex systems and the Santa Fe Institute, you know, in my earliest days, most of my time was taken up with sport. I was a competitive gymnast as a youngkid and then fell in love with Olympic style wrestling. And that consumedmy life really from my early teens into my twenties and was also a gateway for me to see the world. I was the alternate for the Olympics, traveled all over the world, representing Canada, I'm from Montreal, Canada, and just had a fantastic time pursuingthis strange form of excellence which is friendly combat. And as I was wrapping up that particular journeyand trying to figure out what I want to do next, I had this inflection point where I had to decide I was retiring at the ripe old age of 25 niece or ears malformed from years of wrestling what comes next. And a couple of things were happening at that 0.1,

Tyler Marghetis  (6m 44s): I was moving away from sport andreally wanted to finally try to make a go at it as a scientist. I'd always dreamed of being a scientist, but you know, just. I didn't have scientific role models in my life. It really felt like a stretch. The other thingthat happened was, you know, in my mid twenties, I realized I was gay and had to go from dating women to sort of inhabiting this whole new social identity. So I experienced a number of like pretty severe ruptures of social, sexual identity. I came out to my family, oh my God. And then my professional identity basically a pro athlete, it was funded by the Canadian government to some kind of scientists. I didn't quite know what kind of scientists to become next. And then I discovered cognitive science, which for mebrought together all these different things. I was interested in;The brain language, culture interaction, and thiskind of beautiful systems, complex systems, the perspective on all of those in one of research practice. And so that brought me from Montreal, Canada, to San Diego, California, all the way across the continent to do my PhD in cognitive science. And while I was doing that, I always had my eye on this world of complexity science of complex systems, because that was really the perspective that I felt fit most naturally with my own intellectual inclinations. And so after getting fully certified as a doctor of cognitive science, it was really a dream toend up here at the Santa Fe Institute where I could finally let my complex systems freak flagfly, and didn't have to pretend that I was just your run of the mill cognitive scientists interestedin individual psychology. I could be completely transparent about the fact that the issues that animated me were really issues that go beyond the individual that even go beyond the human and are really questions about complex human social systems more generally. And that's been my joy since being here. 


Michael Garfield: It seems like a lot of people come out of the closet as interdisciplinary transdisciplinary. That kind of thing. 

Tyler Marghetis  (8m 54s): And it's arelief and you see bodies relaxing the same way that in my own experience of coming out as queer, you know, all of a sudden I slept better. I feel like Iwas taller. You don't get your whole embodimentchanges. And you see scientists come in this sort of slinking into the Santa Fe Institute. And they were like, well, I guess I'm a physicist, but really I'm or, you know, I officially am a sociologist, but really I'mand they finally just have that freedom to be themselves. 


Michael Garfield: It was funny. I was on the other end of the spectrum. I was just talking to a friend who is considering quitting her PhD program at a rather esteemed university because she came into it with a real clear, strong sense of how freaky she was and how big the questions she had really are. And that she's been suffering and she acknowledges must be some kind of psychosomatic stress-related chronic disorder now two years into her PhD.

And she's like, I think I have to quit in order to get my health back. So, I mean, clearly this is not what I expected to talk about today, but I do think that in so far as your work explores the relationship between the way that we think about things, the way we talk about things, the way we enact them in our environments, in our bodies, I suspect we're going to keep bumping into this fundamental relationship, or perhaps even kind of like non-duality, if I may, between the way that we are in our heads and the way that we're allowed to express ourselves in the effects that has on the way that we relate to one another.

So now that you wrestle ideas instead of people, why don't we wrestle this piece on jazz and on the application of an ecosystemic metaphor to what's going on in jazz and the kind of collective cognitive activity that we see on display in improvisational ensembles. So talk a little bit about the inspiration for this piece and why throughout this piece, you continue to articulate these questions in a way that makes it seem like you're pushing a kind of daring proposal, which is that this analogy actually holds, and that it's not as ridiculous as it may seem to some people.


Tyler Marghetis  (11m 21s): First of all, the inspiration is that I like doing science with friends and Matt Setzler my co-author of that paper as a buddy and a wonderful cognitive scientist, as well as a wonderful composer and jazz saxophonist. So that's part of the motivation, but really the bigger motivation is that I have a couple recurring puzzles mysteries that I sort of carry with me throughout my research. And those include things like, why did we get stuck in ruts in our thinking and our activity?

How do we break out of those? And also as you've been hinting at, what's the role of the body sort of our fleshiness in those ruts and those ruptures. So that's why a lot of my early work was on mathematics because that's a place where people get really stuck in their ways. And then all of a sudden someone has a breakthrough. There's a new proof and they radically reconfigure their understanding. And those issues really show up in a fun way and improvise jazz on this wonderful short timescale that makes it much easier to study.

So in free improvised jazz, there isn't a notated score that is brought into the performance. Most of the playing emerges spontaneously out of what the musicians are doing with each other. They're riffing off each other. They're in conversation, they're coupled, they're decoupled. And out of that initial cacophony, you get sometimes really interesting sounds. And those sounds stick around for awhile. They become entrenched maybe for a minute, two minutes, three minutes, they settle into a rut or another word that I use as they sit onto a regime or a sound world.

And then suddenly seemingly out of nowhere, they completely reconfigure what they're doing and they end up somewhere else. And so for me, this was like a prototypical example of this recurring tension that I see throughout the human experience between these really, really stable ruts or regimes that we get into. And these moments of sudden radical reconfiguration. And so jazz was the perfect case study and also a heck of a lot of fun because jazz musicians in general are just more fun to study than video of mathematicians working on proofs at a Blackboard.

I love mathematicians, but video data of mathematicians, less exciting than smokey basement jazz club video.

Michael Garfield (13m 49s): So, yeah, so reading this paper for me looming over my reading of this paper was the conversation I had recently with Deborah Gordon at Stanford, who studies distributed computation and ant colonies. And she makes the point that contrary to the way that we were thinking about ants, maybe a few decades ago, it's very much like a jazz ensemble, that the roles are mutable, that there is no score in that we were bringing this kind of managerial mindset or a classical symphonic mindset to the study of these systems that figure things out in a very ad hoc kind of way.

And consequently it's like, yeah, there's no manager like the queen is not telling people what to do. I do want to circle back to the question of jazz and that particular mode of distributed cognition and its relationship to these other kinds and like the ecological influence that lead to one strategy over another strategy. Because what we regard as improvisation might be kind of the same thing that we're seeing going on with composition, but at a different timescale or spatial scale, but that's all sort of a meta on this paper.

And we have a responsibility to actually talk about this before we leap into that. So it seems like the place to start here would be in the precedent set by people like SFI, external professor Marten Scheffer talking about what is actually going on at these thresholds or these transitional moments and how it is that we can identify the features that we can look for to anticipate them. So like setting a little bit of laying out some of the core concepts there and then how you and your co-authors sought to identify the features in the music that you were examining that would allow you to kind of quantify all of this.

Tyler Marghetis  (15m 48s): So Marten Scheffer is an ecologist and he, along with a number of different ecologists have been trying to identify generic early warning signals that an ecosystem is about to undergo some kind of critical transition. So you can imagine a lake that goes from a really healthy, thriving, clear watered state to one where all the fish die off and you get a sudden catastrophic algebra bloom.

Can we know that that's about to happen and what those really clever ecologists have done is taken some technical tools that were originally introduced in statistical mechanics, sort of physics broadly looking at when we can predict phase transitions. And the idea is that when a system is perched on the edge of one of these transitions, it's lost resilience in some way. And one way that you can test for that is you can poke the system.

So imagine the lake example. You go in, and maybe you kill off a bunch of the fish, or you add a whole bunch more and you see how rapidly the system is able to bounce back to return to its healthy, happy functioning state. And if you sort of measure that return time, the time it takes for the system to bounce back after you poke it, that gives you a good sense of how resilient the system is. You want it to sort of really rapidly be like, okay, you poked me, but I'm back.

I'm back to usual. A lot of systems that we want to study, we don't have the ability to go in practically and poke them. It would be irresponsible to poke a lot of like big, healthy functioning ecosystems. And so what you can do instead is you just let the system sort of work on its own. It's just sort of like living out its life. And you look at the noise structure of the system. As it bounces up and down, just on the basis of natural noise in the system, there are, it turns out some recurring measures that you can calculate that tell you how resilient the system is.

So you can look at auto correlation or variants or flickering. These are sort of technical terms for different calculations you can do that can give you an idea of how quickly the system forgets these pokes, these prods and returns to its natural resting state. Now, my idea was that these measures of resilience might work just as well in the quote ecosystem of jazz improvisation. So really drawing on those ecosystem metaphor when really that's sort of a way of speaking. What I want to say there is that in jazz improvisation, you have multiple elements that are interacting with each other in a distributed way.

And I could have called that an ecosystem or an economy, or just flat out called it a complex system. But the idea is that in these kinds of systems where you have distributed elements interacting in nonlinear ways, you can sometimes foresee this loss of resilience that precedes a sudden catastrophic, critical transition. And so we set out to try to use the tools that had been deployed so well by folks like Marten Scheffer and others for natural ecosystems to see if they would work just as well for this human social, cultural, technical, jazz ecosystem.

Michael Garfield (19m 11s): Now, if I'm understanding this correctly, one of the main differences between this sort of experimental poking of a forest or whatever, and what you're describing here is the difference between exogenous and endogenous disruption. So in a way that strikes me, this is more similar to say a model of technological innovation, where it has to do with the relationships between the members of the ensemble, rather than say a heckler in the audience.

And although there are great videos of Jacob Collier are responding to people whose phone goes off during a concert or whatever, incorporates it into the play. And he manages to just stay on the rail while acknowledging that that's happened in a really clever way. So I would like to talk a little bit more about the two factors that you're looking at here ,increased variability and lagged auto correlation. So this is a whole lot clearer to me looking at the figures in this paper where you've managed to put this musical data through a series of transforms so that you can kind of see the four members of this jazz ensemble and see in a really stripped down low dimensional way of kind of how they're relating to one another.

But yeah, unpack that a little. 

Tyler Marghetis  (20m 31s): I mean, so the tactic we took was to transform the music they were producing into a trajectory through this high dimensional space of sound. So now instead of just having audio that we're dealing with, we've transformed the performance into kind of like a journey through space. So they start off in one corner, they may be bounced around there for a bit. And then by the end of the performance, they might be an entirely different corner of this high dimensional. We can imagine just picture a room, right?

So the walk in by the door, they're hanging out by the door a bit, then they go over to the corner, they're sitting on the couch and by they I mean the sound they're producing. Once we've done that, all of a sudden we have a whole bunch of mathematical tools because instead of just a bunch of sounds that were sort of subjectively appreciating, we have a trajectory, a mathematical expression of what they're doing. And the idea with increased variability like autocorrelation is that you can look at how that trajectory through musical space is behaving and whether it's highly staple.

So very low variability, they're basically just doing something very, very similar over and over again, or highly variable. So even though they might be staying in the same region of sound space, they're actually more and more sort of diving out and then coming back. They're playing something that sounds really different. And then returning to the thing they were doing before. And then that mathematically, it looks like increased variability in this trajectory, through the sound space.

Michael Garfield (22m 7s): And it strikes me that that's at least geometrically similar to what you see again in like ant foraging, how the loop out exploring for new resources and then somebody will find something and then the whole nest sort of changes direction at that point, all the other ants follow and having organized a group improvisational exercises in my past life in Austin, you feel that you can tell people are getting kind of bored and then they start testing things and then everyone notices and latches on to something.

But it's curious because in this piece, you kind of suggest that we don't expect to observe this kind of thing in composed scripted music. And yet when we look at like the harmonic structure, as we move through a piece of music be at classical, this whole build and release, something becoming more and more dissonant before it kind of condenses into a new form or an electronic dance music, there's the buildup and the drop. And so I'm curious if those seem substantively different to you than what you're observing in the ensemble, or it's not merely a structure that we observe in kind of like real-time improvisational collaboration, but it has something to do with like the way that we process information and the way that we organize narrative structure and the way that we move through various spaces at whatever timescale.

Tyler Marghetis  (23m 47s): And so I think in the compose case, you're completely right that compose music is playing off a set of expectations of cognitive responses that we're likely to have so far as we may have evolvedto be sensitive to this kind of loss of resilience in a system before an exciting, critical transition. It's entirelypossible that composers, maybe even unconsciously have been building inthese kinds of signals into their music as a way of communicating to the listenerthat something is about to approach. On the other hand, I don't think we would see the same kind of loss of resilience and compose music that we see in jazz at the micro structural level, which is reallywhere we see it with jazz. We see it breaking down on the millisecond to millisecond level where all of a sudden what's happening in the present moment is much more tied to what they were doing a secondago. This is lagged autocorrelation, this is memory. So the system is building up a memory, what it was doing before it's taking longer and longer return to its happy spot, right? It's the sort of that natural attractor. And I don't think we would see that with composed.But I want to circle back to your point about the ant going out and exploring, because I think that's also really interesting and there, a lot of folks woulddescribe that as a trade-off between explore and exploit. So a lot of systems engage in and by systems, I mean, say like a foraginganimal will find a patch of food and then it's, you know, chowing down. It's a buffet, it's super happy, but it needs to make a decision. How long does it stay there?

 As the food begins to run out. When's the optimal moment to be like, okay,yeah, this is great, but I'm running out soon. I should probably find the next berry bush or whatever. So when it'shanging out and just eating, that's the exploit phase, it's exploiting the food and then the explore phase. And when it goes out,which is costly right there, I have to move through space. There's a metabolic cost. That's beenstudied a lot by biologists and ecologists,whether foraging actually lives up to the optimal trade-off between exploiting a food source and exploring for a new one, we can ask whether musicians do the same thing or storytellers or mathematicians. There was a similar trade off that the ant colony needs to make between exploiting where it is right there right there, sort of thesecollective free jazz musicians, really riffing on a particular sound world and be like, this is fun. And then deciding, okay, when is it not paying the same dividends that it was before? When should I begin to explore some other region of the sound space? When should the little ant go out and start exploring somewhereelse?


And you brought up boredom, which I think is something that's really interesting about human social systems that you don't necessarily have with natural ecosystems. So in a natural ecosystem that can exhibit these kinds of critical transitions, this critical slowing down, which is what you see before with this loss of resilience. You don't have individual fish who are like, okay, we've been in this particular ecosystem, stable state, we've been in this basin of attraction. I'm bored.

I really want something exciting. I would love like a mass die off and a bloom of it. Like that sounds way more fun. That doesn't happen. You don't have individual that have a Metta image of the entire system and goals and aspirations for that system. Should do you do have that with jazz musicians where the individualisn't just sort of riffing on its own and unthinkingly coupling withthe other players, they have a vision. And if the system has been stabilized in area for too long, they can get bored because they're interested in more than just maintaining their local dynamics in some sort of stable way. They're also trying to impress an audience. They're also trying to be interesting. And that's what makeshuman social complex systems so interesting is that you often have these local representationswithin the individual, within a book, within a play of the collective of the society of the performance andthat sort of multi-scale structure where the local partsend up representing what they aspire the whole system to do is something that I think is really unique to human social systems. 


Michael Garfield: Oh, good. We just walked right up the ladder to the sort of meta that I wanted to ask. So, you know, thinking about jazz as a strategy, this was one of our undergraduate researchers with Abby about she wants to study a music project and I was suggesting looking into the composition and improvisation and kind of an evolutionary dynamics thing. So in so far as any anatomy or technology is an adaptation, is it response to a given environment and therefore kind of a hypothesis or embodied model of the world, right? Jazz is saying something about the world that it merged into or emerged through.

And certainly, many people have said very eloquently that jazz, as we understand it in the United States emerged as a response to the trauma of the world wars and a challenge presented by industrialized warfare to the model of the world that we had, the linear narrative of the progress of modernity. And so when we talked with Laurence Gonzales on the show about his book, Surviving Survivaland on trauma, the relationship between trauma and creativity, the fact that jazz musicians are playing off a score and are responding at this whole other timescale to these minute variations in the environment, seems like it's symptomatic of the fact that we had to throw the script away, that suddenly Wagner looks like a Nazi, that like he was, but like when I spoke with David Krakauer about mass extinctions and market crashes in episode 29, and we talked about how a high beta trading strategy, this more like exploratory mode of investing and how that's related to in mass extinctions, you see this mature ecosystem with like dinosaurs and other megafauna, you know, very narrowly specified symbiotic relationships.

And then all of that comes crashing down. And what survives are generalists that are actually horribly inefficient in one of those systems that you in a mature ecosystem, be it ecological or cultural, you find a lot of specialists, but then as the unpredictability of the environment goes up and up and up, then suddenly that inefficiency pays off. So it's specifically like free jazz is like this very narrow subset of jazz and you address that in this paper.

But, you know, I just curious what you think about all that, because I'm inclined to push for an even deeper embrace of this analogy than you seem to in the paper. And like in particular, the way that you just said, as you say in this paper that one difference between humans and nature, as we're talking about them here is that we don't have these centralized transitions in nature. And yet here we are in the Anthropocene where you have mega billionaires that are capable of like leaving an impact on the geological record.

And that's like the ultimate invasive species. And like, it does seem to blend together for me in a different way. 


Tyler Marghetis : I won't argue with you about that. I mean, I think there are a ton of really productive analogies between these. I do think it's funnyto look at the history of everyone's favorite analogy. There's been a bit of a discussion within the Institute over the last week about this recurringphrase, you know, everything has a blank.


This was a meme that was contrastingAaron Clauset, which external faculty at SFI with Cris Moore, faculty and residents. And I think Cris Moore was saying nothing is a network. And Aaron was saying everything is a network or vice versa.

Tyler Marghetis  (31m 45s): And that prompted this fun internal reflection about as long history of everything asa blank statement. And so therewas a period where people were saying, you know, everything has an ecosystem. And I think I'm part of that tradition in saying that, you know, a jazzensemble is an ecosystem, but prior to that, there was everything is an economy and who knows what the next metaphor is going to be. And so if I resist sort of a too strong identification between jazz and natural ecosystems, it's only because I recognize that our favorite modelsystem is going to change. And like with anymetaphor, certain things become clearer and other things become cloudier. And so in saying that jazz is like an ecosystem or is an ecosystem that foregrounds the bi-directionalnonlinear relations between different components and probably makes hazier other aspects of jazz. That might also be interesting, but you're right. That in bothcases you have this really interesting nesting of timescale. I think you were hinting at that a bit with your discussion of mass extinctions, where one thing that a mass extinction does is it resets the accumulation of timescales. It resets that lamination of deep history, moderate history, recent history, and all of a sudden you get, you know, these generalists because you don't havethese wonderful, arroyos these wonderful river beds that have been laid out by the long history ofthe ecosystem. And you definitely do have that in jazz, even in free jazz. So yes, in free jazz,they don't have a written out score that they're riffing on,but there is a long history of practice and norms that all of these players have internalized. You can't just geta a bunch of random musicians together and be like play. There's a genre, there's a set of expectations and those have a history.and what I think is reallypowerful about this ecological metaphor is it sheds light on those multiple timescales.So we have the micro timescale of the saxophonist picking up on smalllittle variations in how the drummer is playing. Then you have like a miso timescale of the hopes and aspirations of these players for what they want to do withina piece. And then with that a gig, and then also a lifetime of training, and then also a cultural historical timescale of how those drums developed. And in that paper, we really focus on the micro time scale. But I think there's a really interesting story to be told about similar critical transitions in aesthetic regimes over the long historical timescale of music. And what really excites me is a finding generic mechanisms that apply equally to the micro timescale of the millisecond to millisecond variation in play, as wellas to the longer socio-historical timescale as you said, this sudden visceral response to the horrors of the world wars that gave rise to something like jazz, which itself is like a critical transition in the history of music, but on a very different scale. 


Michael Garfield: So this is great because now we're getting into a conversation I've been, I guess, prosecuting on social media, which is about this phrase, the death of the genre. If I call back to the conversation I had with Geoffrey West and 35 and 36, and you know, this ominous graph that he draws of the finite time singularity where, innovation precipitates, it's a crisis that is then solved by innovation, which resets the crisis clock.

But now the clock is moving faster and we just keep doing this over and over in this like super exponential curve of delayed disaster. And this is, you know, much like Simon Levin, just co-authored a piece in PNASon using evolutionary models for financial markets. And they were talking about a very similar thing in innovation and finance, where we now have these high-frequency trading algorithms and the flash crashes that they induce, things are moving at such a pace that it sort of defeats our ability to even adequately model them, which sounds a lot to me like what people are getting at when they say the pace of recombinant change now in a global musical context, where everyone is exposed to everything and it's remixing constantly doesn't afford the kind of subcultural insulation that allows for stable genre categories.

And it looks more like horizontal gene transfer among bacteria than it does the kind of stable you carry euchariotic inheritance of Darwinian evolution as kind of commonly conceived. So I guess what I'm getting at is like, it seems like to some degree free jazz has been released into the water supply. And I'm curious where you might push against that or to what extent you think that that holds that. We're kind of at a point now where in spite of the fact that yes, free jazz is a genre that the notion of genre now has to be bounded or constrained or contextualized in a certain way to even mean something.

And you know what that means in terms of the fact that we're actually inside one of these critical transitions that your paper models that the critical slowdown is happening all around us. 


Tyler Marghetis: I am not a historian of music. And so I will speak softly, but two things, one, all of the examples you just gave or of catastrophic negative transitions. And I think it's important to remember that often these critical transitions are beautiful and transformative and elevating.

So think of a great artistic breakthroughthat suddenly leads to a period of great productivity or, you know, a mathematical insight or two people falling in love. These are all examples of critical transitions that are really quite fantastic. And I think on the surface can be modeled in really similar ways to Geoffrey West's singularity, these kinds of horrific market disasters. But I think it's important to remember that they're all so are really fantastic, beautiful, criticaltransitions.


Michael Garfield: Honestly, I don't mind the death of the genre. It means that we get know as long as we have algorithms to recommend me music. So I don't have to try to like figure out in a record store where to go for what I want now. It's like, there's more excellent music now than there ever was. 


Tyler Marghetis : The other thing I'll say is that in a jazz performance, you don't have pieces that lasts two seconds and you don't have pieces that last for days, theyseem to fall within this range of two to 40 minutes. You know, if you're really sort of riffing hard. 

Likewise with things like genres or other cultural objects, the brand, the scaleof those objects emerges from the culturaland that can change. And so when we talk about the death of genre, I think we're actually talking about a change in natural scale. The scale of the cultural system has changedso that the right way, of course, graining people's cultural productivity is no longer the scale that we're used to from our younger years where we sort of had an expectation about the right way to slice up cultural space.
I think it's changed. I don't think there areno longer naturally emergent divisions, aesthetic preferences, clusters of interest. Thosestill are there absolutely there just on a slightly different scale than we're used to. And, that's a little uncomfortable because we're used to knowing the rightscale to look at, to pick out the genrehas changed. And I think that's fun. And I think my betis that if you jumped in your cryogenicfreeze and machine froze yourself, came back in a hundred years, people are still gonna be talking about genres, but they're just going to be on a scale that's unrecognizable to you, or to me, I think we're in that process of shifting temporality of shifting scaleat which we experienceproduce and sort of classify artistic products generally, but especially in music. 


Michael Garfield: That really strikes me as a kin to the work that David Krakauer did on the evolution of syntax back in the day and that, like, if we are looking at this recombinant creative explosion, it's in response to gear shift here. I guess shifting the relevant scale that looks a lot like the shift from trying to remember every word that humans have to remembering a few rules and a few words, and like knowing how to put them together in a more interesting way.

And then at that point we can specialize because then your group over there can have words that I don't need and so on. But then again, like at that point who's doing the sorting and we cannot expect anyone to actually know all of the different, highly granular genres that were created by the downward causal pressure or whatever of this new domain. Anyway, I don't know that could be word salad. We're at a pretty good point where we can get into this other paper, which we're only going to do the two.

Michael Garfield (41m 13s): So this one you led with Kate Sampson, Dave Landy, the complex system of mathematical creativity, modularity bursting times, and the network structure of how experts use inscriptions and this rhymes in an interesting way, the jazz piece because you're looking at how people are thinking out loud. Or rather, like in a visual way, the equations on a chalkboard you're coding and examining video, but this is largely about zooming out from the jazz ensemble that might be going on in someone's brain.


And then looking at it, how that creates a network of symbols on a blackboard and then how that person's writing and attention moves around in that network. Maybe I've just spoiled the whole thing. 


Tyler Marghetis : There's the punch line. I will say in a fundamental way, this hearkens back to the comment that you made at the top about the role of our bodies in thought, and that's been a real through line of a lot of my work dating back to my PhD days, which is that even if you look at the most rarefied abstract forms of human reflection, you find that the body is there front and center, and thisis especially true in mathematics.


The received vision that we have of mathematics is that it's pure rationality detached from our fleshy emotional bodies. Who do we think of when we think of, you know, thesort of outer reaches of mathematical reasoning, it's like Stephen Hawking,a person who in many ways did not have access to his body as a tool for thought. And sothe fact that that is a political image of mathematical reasoning says something aboutour received cultural pictures of how math works. But if you actuallygo out and look at how math done, it turns out it is par exellence, an example of manual labor, right? It's themost manual of all the labors years ago, I sawthis ad for a government retraining program and it said something like in the future, there will be no manual labor, but the picture was of a computer programming typing with his hands. Let's not forget whatmanual labor means. It means working with your hands.

Michael Garfield (43m 43s): And there's sucha cultural judgment associated with the, using our bodies for labor in general. We value white collar workers who don't sweat, who don't use their bodies in our cultural videos. Sothat's sort of the cultural image. And so we forget that, you know, whenever we're doing something we're doing with our bodies, right. We're biological organisms and that's true, no less of mathematics. What does math look like? It almost never looks like Stephen Hawking sitting in isolation in his chair. It looks like often a small group of people scribbling away at a blackboard or whiteboard or here at the Institute on our windows with markers. And we're being our usual fleshy mammalian selves. And even the case of Stephen Hawking, there's this wonderful ethnography of Stephen Hawking by the sociologist Helene Mialet who looks at how has he been Hawking is able to do at all. And it turns out he does it by relying on the bodies of other people, of his students. So Stephen Hawking would recruit a new student every year and would give them these short commands that would guide how they should scribble draw diagrams, write equations on the blackboard. And he would sit back and inspect what they were doing. So he didn't have access to his own body due to mathematics. So he had to recruit the body of another. So that realization that our bodies are core part of even the most abstract thought, even the most arcane regions of mathematical reasoning has really a lot of my work. And a lot of my research has trying to quantify what exactly our bodies are doing in this quote unquote abstract realm of thought. And that's what we're trying to do in this paper. We're trying to use the tools of complexity science to quantify the use of people's bodies as they were working on fairly tricky proofs. These were math experts. You know, most of them were finishing up a PhD or on their route to a PhD in mathematics. And again, adopting this ecological metaphor, we were trying to figure out what within the natural ecosystem of mathematical reasoning, which is one or more bodies out of blackboard where they're scribblingand erasing and pointingand looking and talking and doing all the things that are part of the canonical mathematical situation.


Michael Garfield: So the thinking in space, right? That's a big piece, actually. There's several of your other papers get at this and your work with Nunez, right? Like you did your PhD study, Where Mathematics Comes From, really interesting, cool book. If folks want to dig more deeply into that, but like, you know, for, for the sake of time, like let's focus on how you and your coach analyzed the way that people were writing out their thoughts in the two dimensional space of a blackboard, his dad has networks in order to formalize it.

And then the patterns that you found in those networks, because that, I think gives us a place to anchor this piece back into the first half of this conversation and talk about the flights of the imagination. 

Tyler Marghetis  (47m 14s): And so the methodological tactic we adopted here was a focus oninscriptions being put on a blackboardand to treat each new inscription,whether that's an equation or a as one node in a larger network of inscriptions. And so the vision we had was that when people start working on a problem, you know, they might just write out the statement of the problem. That's one note, and then they think, okay, maybe I'll draw a picture, drawing a picture, always a good idea. When you're trying to solve a problem,a little diagram, that's another note. Then they can look back and forth between those and that act of shifting your attention between those two nodes. That's the edge. And so what we could do is look at a dynamically updated network that was changing over time. It was gradually accumulating, more and more nodes as people were introducing more and more inscriptions to their quote ecosystem of thought. And what this allowed us to do is to step back from whenever they're thinking, which we can't see inside their skulls. We don't have a cognito scope that allows us to extract their thoughts. And instead to focus on, as I said before, the manual labor of mathematics and this wonderful dynamic structure that they're creating in front of them that seems to be really important because we all do it when we're doing math. We fill up whiteboards or blackboards or windows with inscriptions. We want to see what does that actually look like? What's the structure there? And so we were able for all of these different mathematical experts, working on these problems to build for each of them, a network representation of how they'd gone about solving the problem, and then ask questions about the structure of those networks and the dynamics of people's attention as they're shifting their interaction from one diagram to a different equation, to another word, to another diagram within this network representation.

And really the metaphor that I had in mind was of niche construction, the way that some organisms transform their worlds, spiders, building webs, animals, building dams, to completely transform the local terrain and to think about mathematicians as people who engage in this kind of cognitive niche construction, changing the terrain of thought so that some insights become easier and others become more difficult.

And looking at those notations as the mathematical equivalent of the spider web or the dam that's being created by the organism to changetheir niche. 


Michael Garfield: Well, I mean, certainly, you know, it, it calls to mind that hilarious fictional video, or it's rather a, a kind of a remix fictionalized remix of the old video of we gave all these different drugs to spiders and here are the effects. I'm sure many of the listeners to this podcast have seen that excellent Quantaarticle from a few years back about the web as a cognitive extension of the spider's own brain.

And so I don't feel like you're making a huge analogical leap here at all. 


Michael Garfield (50m 27s): I mean, from, from orbit, everything looks really close. So from that aerial view, two interesting patterns emerge here that you figure in this paper and they're characterized by what I recognize actually as musical terms, clusters, which again, a shout out to the musicology and complexity working group. You think about tone clusters and just kind of mashing your hand on the keyboard. Everything's really close versus loops where things are a little bit more spread out and that's sort of orthogonal, unless you're like Dimitri Tymoczko and you're actually mapping this stuff on a circular object.

But one network is really sort of dense and a one network has these sort of long linear arcs in it. And yet these are two different approaches to solving the same problem. And I'm curious what that says to you about the way that different people solve these problems. And then also how it might relate to a talk to a link to in the show notes that Simon DeDeo I gave last year on explosive proofs of mathematical truths, where he's talking about not these solving of an equation per se, but the formulation of a mathematical proof and how rather than it being this linear thing, you can actually represent them as networks.

And then you can knock pieces of that proof out. And the whole proof still holds. Whether you think that viewing this solving of a mathematical problem in this way, whether certain approaches are more or less brittle to disruption in the way that the day I was talking about certain paths to reprove being more robust.

Tyler Marghetis  (52m 5s): I will say, first of all, the patterns that we saw weren't necessarily individual differences between people, but more so different patterns that we would find within the same episode or problem solving session. So a single person might produce a whole cluster of notations that were all tightly interlinked so that they would move fluidly from one to the next, from the diagram to an equation that might be describing something in the diagram to a English phrase that they'd written out.

And that very same person might also produce these loops of inscription, where there was a natural order that they would travel through. So if nothing else, I think that's a nice quantitative demonstration that the way that we teach kids to do proofs in school, which is you start from the axioms and then you write out linearly from top to bottom, how you want to work through. That's not how mathematicians actually do math. It's a much more beautifully tangled process with different notations entering into different relationships with other notations within the larger quote ecosystem of the blackboard.

So the first point there. Second point is I loved Simon's talk. And I actually went back and looked at our data to see if we found some of the same patterns of out and in edges, in not the sort of like statements or deductions that people were making, but their use of inscriptions. And it wasn't a perfect match, but it looked very, very similar to what Simon was reporting. So in the same way that Simon found that you can get these robust proofs if you have this nicely unbalanced relationship in how different statements are relating to each other. We found a similar pattern, this is unpublished stuff in the relationship between different scripts, which makes sense, right? Because these inscriptions are corresponding to some thought or statement or claim or inference, but it's nice to see that parallelism, if not like a strict isomorphism between how people are setting up these proofs as abstract inferences and then how they're actually structuring their world to arrive at those conclusions.

Michael Garfield (54m 26s): So to a point that you made just a moment ago, you see examples of each in any given mathematicians approach to solving this. It strikes me that this goes back to what we were saying a moment ago or a few moments ago about the tension between explore and exploit. And that the sort of bursting in the patterns that you're observing you say in this precise amount of modularity likely reflects both the demands of the particular problem and the stochastic situated decisions.

And I'm thinking, does this tell you something about the level of comfort that a mathematician has with the particular problem or rather like, are they building the bridge very slowly and carefully and or are they throwing these large ropes. You know, at what point do you realize you're stuck and that you have to back out and, and take a completely different approach? Again, there does seem like some kind of a family resemblance again to what the pattern we were seeing in the way that the jazz ensemble moves through its own kind of search space of interesting new musical possibilities.

Yeah. And so, yeah, I guess when would I say this is like, what does a healthy mathematical ecosystem look like. If we were engineering these things, how would we want optimally to set up this ecosystem of inscriptions so that practicing mathematician would be most likely to arrive at, you know, a really fulfilling insight and that's exactly what we're doing right now. So one of my PhD students, Shoddy Tabatabian is looking at these network structural and also these sort of more dynamic measures like bursting us that you mentioned and seeing whether we can use those to predict when mathematicians are going to express an insight, when they're going to have that in some cases, a literal aha moment when, you know, in the videos, they're at the whiteboard, they're struggling, they're huffing and puffing. And then, you know, there's a beautiful park. And they said, I got it. When do those show up in relationship to the dynamics of inscription that have been going on before? Can we predict when that's going to happen based on the quote healthiness of their notational niche that they've set up, still working on the analysis. But what I suspect we'll find is something really similar to what we found with the jazz musicians which is that we can find these system level indicators that the jazz musicians are about to move into a new regime of sound production and the mathematician or the mathematician brain, body blackboard system is about to shift from a regime of confusion and frustration to one of fulfilling insight and realization.

And so there's definitely that really, to us, very explicit parallel between the micro level ruptures, the critical transitions of the jazz performance and these slightly longer timescale rupture or critical transition in the mathematician.

Michael Garfield (57m 36s): I could be getting this completely wrong, but it strikes me that what you're talking about here has a relationship to maybe parallel studies in the network dynamics of virality. You say here that the predictor with the largest relationship to burstiness and the only one that was statistically significant was modularity more modular inscription activity with communities of densely interconnected inscriptions was associated with more bursty temporal dynamics. And, you know, this reminds me a lot of, I cannot track the citation down to save my life, but I remember a few years ago saying that there was some research on what actually leads to a viral meme and it had to do with like saturating a local network.

And then at that point, it sort of able to burst out. And the way that you're describing it could be somewhat analogous to the moment at which society at large has the idea, where it's on its own little island, mutating and then something clicks and suddenly it has percolated through everybody.

Tyler Marghetis  (58m 41s): One difference here is that the network reputation we have of mathematical activity is much more serial and much less parallel compared to a network representation of virality, where in a network representation of orality, each node is a person who may or may not have adopted a particular meme or become interested in a musical genre if there was still exists while in the case of the mathematician, we're really tracking their attention as it shifts step-by-step from one inscription to the next.

So that's perhaps a superficial difference, but it means that the mathematics of how we make sense of this is going to be slightly different. I will that in some of my other work, and this was a paper that we were maybe going to talk about today, but I don't think we'll have time to talk about it today is I am really interested in how these critical transitions in abstract thought occur at the even larger scale of entire societies or linguistic communities and there this metaphor of virality is absolutely germane.

And so you mentioned George Lakoff at the top of the show, who's written and thought a lot about the metaphors, that structure, our thought, and that get into our language. And so for me, what happens with the jazz musician, where you have this critical transition from one sound world to the next, and what happens with the mathematician where you have this rupture from confusion to insight is in a certain sense, similar when you wear the foggy glasses of complexity science. Those two processes are really similar to what happens when an entire community goes from thinking and talking about, say the nature of time or justice or right governance to an entirely different one. And to me, the interesting questions are like, what are the generic mechanisms that allow us to understand and predict when this kind of human social system is going to go over the top of the waterfall and end up in entirelynew ones?

Michael Garfield (1h 0m 46s): Well, I mean, it would seem that that has, when you fall over the edge, seems to have everything to do with where your body is and what it's doing. And we we've made it all the way back around in that regard. Well, okay, Tyler, this has been awesome. You've hinted at some of the direction that these inquiries are taking. That paper in particular had a rather extensive list of how you might see this kind of thing evolving over time in ways that you didn't actually apply in the study.

What are some of the greatest unanswered questions for you that we haven't already touched on so far in this conversation? We'll leave people hanging.

Tyler Marghetis  (1h 1m 29s): So for me, I'm really excited about stretching this work from the millisecond to the 10 minute, to the life, long creative insight timescale. And so I'm working with this wonderful data set that's been collected by this fantastic historian of art that has documented basically everything that Pablo Picasso ever produced in his life. And, you know, Picasso is this person who's constantly reinvented himself over and over again.

He's all of a sudden he's painting everything blue and then pink and rose. Then all of a sudden he's doing cubism. And the question for me is, do we have similar dynamics on that scale of sort of lifelong creativity that you get on the micro millisecond scale of jazz improvisation? How are those similar, but maybe more importantly, how are those different, like, what's the cool stuff that happens when you're talking about lifelong creativity that isn't that player on a short timescale.

And one possibility is that when you're a jazz musician riffing in a smoky basement, the sort of larger cultural trends that are happening outside are changing so slowly that you're not necessarily impacted by that. While someone like Picasso who's being creative and entire life span is ritually and productively entangled with other lives, other social trends, with world wars. And I think that entanglement of largely independent, but mutually interdependent systems is one of the really exciting places to look at these kinds of human critical transitions.

These cascades from what one community is doing to what another community is doing to what's happening sort of broadly in the newspaper as to what one person is doing in their studio and trying to get some kind of empirical quantitative, nice analytic mathematical traction on that super broad, messy web of influences is what's keeping me up at night these days.

Michael Garfield (1h 3m 38s): Well, if that's what it is, then I wish you insomnia, sir, for the good of all of us, this has been awesome. Thank you so much for taking the time. This is super fun.

Thank you for listening. Complexities produced by the Santa Fe Institute, a nonprofit hub for complex systems science located in the high desert of New Mexico. For more information, including transcripts research links and educational resources, or to support our science and communication efforts. Visit