Higher order math and love with Carlos Zapata Carratalá

Carlos is a founder of the Society for Multidisciplinary and Fundamental Research (SEMF), and a Postdoctoral Fellow and Head of Strategy at the Wolfram Institute, a recently established research institution dedicated to the investigation of the mathematical foundations of computation and the legacy of Stephen Wolfram's scientific ideas. This talk explores his childhood fascination with physics and mathematics towards a multifaceted academic and personal exploration of higher order maths and relations in a quest for a deeper understanding of the universe's complexities. Carlos eloquently discusses the challenges of aligning personal passions with academic pursuits, his evolving interests leading to groundbreaking reflections on higher order mathematics, complexity theory, and their applications to understanding not just the cosmos but the complexities of human relationships, especially within the context of polyamorous dynamics. The narrative weaves together the beauty of scientific inquiry, mathematical honesty, and the deep, introspective examination of human connections, advocating for a boundary-defying approach to knowledge and love.

#semf #Carloszapatacarratalá #higherorderthinkingskills #hiott #love #philosophy #wolfram #andreahiott

00:00 Exploring New Languages to Understand Nature 00:25 Theoretical Foundations and Practical Impacts 01:17 Navigating Romantic and Social Connections 02:30 A Deep Dive into Love, Philosophy, and Mathematics 03:01 The Journey from Philosophy to Mathematics 03:51 Challenging Traditional Academic Paths 07:39 Embracing Multidisciplinary Approaches 08:55 Personal Growth Through Unconventional Learning 10:21 Redefining Success in Academia and Beyond 14:28 The Role of Teaching and the Quest for Knowledge 28:07 Navigating Life's Complexities with a Love for Wisdom 35:47 Reflecting on Personal and Societal Growth 41:21 The Influence of a Father's Perspective 41:35 A Unique Approach to Learning and Curiosity 43:51 The Role of Love and Family in Personal Development 45:15 Exploring Personal Identity and Social Dynamics 52:48 The Journey from Physics to Multidisciplinary Exploration 01:04:28 Reconciling Childhood Curiosity with Professional Ambitions 01:09:18 Embracing Complexity: Higher Order Interactions and Network Science 01:17:15 Exploring Sequential Structures and Their Relevance 01:17:42 From Static Sequences to Dynamic Data Structures 01:18:53 The Evolution from Linear Chains to Complex Networks 01:19:37 Introducing Network Theory: A Foundation for Modern Technology 01:20:07 Hypergraphs: Expanding the Concept of Connectivity 01:22:06 Challenging Human Intuition with Higher Order Processes 01:25:13 The Attraction of Conceptual Engineering in Mathematics 01:29:11 Historical Perspectives on Language and Mathematical Breakthroughs 01:39:36 The Future of Computational Tools: The 21st Century Blackboard 01:45:44 Redefining Mathematical Interaction with Diagrammatic Programming 01:51:36 Calculus as a Paradigm Shift: Implications for Future Innovations 01:56:51 Exploring the Language of Mathematics and Its Impact 01:56:56 Theoretical Foundations and Practical Implications 01:59:04 Interdisciplinary Connections and the Essence of Mathematics 02:00:31 Mathematics as a Universal Language 02:04:39 Personal Journeys and Mathematical Analogies 02:08:16 Exploring Polyamory: A Mathematical and Personal Perspective 02:10:21 The Complexity of Higher Order Relationships 02:30:15 Reflecting on Personal Growth and Relationship Dynamics 02:34:43 Concluding Thoughts on Mathematics, Relationships, and Clarity Carlos Zapata Carratalá's research project website: https://www.arity.science/ The society's website: https://semf.org.es/index.html The name of the society (SEMF) is Society for Multidisciplinary and Fundamental Research A recent paper from Carlos with a summary of his research project: https://www.worldscientific.com/doi/1... Carlos completed his undergraduate training at the University of Valencia and Imperial College London, and then pursued graduate studies in mathematical physics, receiving a masters from the University of Cambridge and a PhD from the University of Edinburgh. During his time in Edinburgh, Carlos worked as a research assistant to Sir Michael Atiyah and a teaching fellow in the School of Mathematics, while also running the Society for Multidisciplinary and Fundamental Research, of which he is the founder and president. His research focuses on the mathematical foundations of science, particularly in physics and complexity investigating the realm of higher arity structures in science, mathematics and art with a particular focus on ternary structures. This deeply multidicsplinary project explores ideas with roots in simple algebraic objects that, due to their fundamental nature, manifest in fields as diverse as molecular biology, token economics, cognitive science, nuclear physics, data science, knot theory, music or game design.

Transcript:

 So the new language would be illuminating these links and give us some way to understand higher order interactions in nature.? We might think of selves as multiple, or maybe visualize life and ecology in a different way.

Yeah, I don't know if I would dare to say that it would change something, but it would certainly expand. Give

language to it.

Give language. That's right. Give language to articulate it. And eventually the hope is that if you look at the pattern of the industrial revolution, it was, so you do this theoretical work, you effectively invent a new language, new symbolic system of calculus, derivative functions, all these things.

And with time you have all this output in practical life. And basically changes human existence forever. In a very humble way, we are in the sort of, theoretical stage in which we are dealing with things that we don't understand well, like the cannonballs in the 17th century. And we're like, okay, how can we model this? And we are beginning to develop the language with this sort of hyper blackboard, as you put it and giving the tools for mathematicians to possibly engage with it in ways that are intuitive to them. We're trying to put ourselves in, into this position of , hopefully ushering a future era of intellectual development and technological development eventually, to understand the systems that you mentioned, like higher order relations in life, how humans relate

  You have romantic connections with individuals. And, if you center yourself in the middle, as we normally do intuitively, you would have a a span of pairwise connections going out to other people, right? If you are in a more traditional partnership, then you have one single connection going out, romantically or sexually or whatever

but if you're in a polyamorous setting, the default is that you're going to have more than one and so that, Doesn't say anything about whether the connections are pairwise or not. Typically people would have pairwise connections which you just happen to know a new person and you develop a pairwise connection. Pairwise connection with that person, but you don't break the connection that you had with the previous romantic partner

so you effectively keep more than one romantic connection going on, but each of them is pairwise now, what you could have is also higher order romantic relationships. There's like triangles, there's groups of four that are in, in engaged, engaged in romantic, which does

exist too.

And not only in a sexual way  📍

📍

Good morning, Carlos. Great to see you. Thanks for being here.

Well, my pleasure.

So this is about love and philosophy, and really it's about trying to get beyond binaries, beyond dichotomies,  which I know is a subject close to your heart . But just for those who might not be familiar with your work yet could you just riff a little bit on this idea of philosophy and maybe relate it to what you're doing in your career, which is a mathematical based career at this time?

Yes, of course. I'm glad that you asked the question about philosophy. I remember being quite young and thinking the word philosophy makes a lot of sense, because, the etymology makes a lot of sense, love for knowledge, love for wisdom and sort of the gathering of knowledge and about the world and about oneself and so on. I learned about the etymology of the word sometime in, when I was 12 or 13 or something. And then I thought, yes, I like philosophy. I like to say I like philosophy because I'm very much in the, in that mood.

I want to, gather knowledge and I love knowledge. And so it makes sense. And then I remember studying philosophy in later years in high school and then in university and being in contact more with the academic. philosophy. I thought it feels like this lost something along the way.

I'm not seeing the same the same vibe that I was getting when I was younger. And I have to say that since, I got involved in setting up events and the society that I'm leading now and so on. We are trying to one of the missions that I had in mind when doing this was we want to regain the etymological origin of philosophy and sort of try and get back to that sense of philosophy.

And of course, academic philosophy is a different thing. It's when you're saying what is academic engineering and what is actual engineering, these are two very things.

As someone who studied philosophy, in school, it can be very difficult to connect those worlds, right? I also have had that experience where even the philosophy I was really turned on by in my teenage years, the reason I even studied philosophy, got degrees in philosophy. Once you start studying it academically, it can turn into a whole other thing. But also, I don't know if you've encountered this in creating.

and setting up the society, but sometimes there's, there becomes some pushback between, for example, if you go into really deep logic and analytic philosophy, then if you start to talk about people that I might've thought of as a philosopher as a teenager, the ones we kind of connect with on a more of an emotional level those might not be taken seriously.

Do you know what I'm talking about in this?

I certainly know what you're describing. , I have to say I haven't, interacted, with sort of academic philosophy as an academic myself. I've interacted mostly with academic philosophers, and I have organized several events that they were involved in and so on.

But I can relate to that feeling from the perspective that when I was a teenager part of my. I don't know, pastime, I guess, intellectual adventures, was to write essays on like metaphysics and things like that. But they were very sort of homebrew. I would not go on and read several books or anything like that.

I would just, think about things and sit down, write down stuff, and then maybe even give it to my philosophy teacher in school. I was just like intuitively putting into words sort of ideas and, like classifying experiences and things like that.

It's fairly elementary stuff. Nothing new, obviously nothing of value. In the grand scheme of the philosophy, of course, but I remember doing it. I was fine. It was okay. Yeah, this is organizing my thoughts. It brings the solace to the complexity of life in some sense, and so on. And then I remember moving meeting academic philosophers and thinking, Oh, wow, these people really have their their dichotomies and their classifications in mind, because, I, they said, Oh yeah, this is no, this is an analytic philosopher. This is a sort of, continental philosopher, all these kinds of things. And I was like, okay, that's completely lost on me. I couldn't really, I mean, it took me a while until I realized, all right, so they are in their academic field and there's all these sort of traditions of thought.

And then I got to this point where. For a lot of my colleagues on they agreed with me in large part. They agreed that academic philosophy was mostly history of philosophy and then a little bit of actual philosophy going on as well. And that philosophy as an activity is really more universal than what academic philosophy is doing, or at least the large chunks of academic philosophy.

So I think my realization more than being placed firmly on one sort of a box, although I was, cause they were telling me, oh yeah, you sound like rationalist, positive, blah, blah, blah, blah. Some tag some tags, , to my profile. So it was interesting that dominated the conversations most of the time instead of actually trying to unravel ideas. And of course, this is mostly due to my ignorance at the time , of the details of all the previous work.

But I did get into conversations where it got very unproductive and I'm very sort of sterile to keep circling around who said what. I said, well, I don't care who said what, but I want to discuss you, the two of us in this room, like what the concept is. And I think I've found a lot of people that say, yes, this is definitely something that has been missing more in, in philosophy.

I think that at least in academic philosophy. And so that's actually, was one of the drives for me to. To identify that there's value in doing academic activity. I can academic like activities in a little bit different way.

You see it as connected to things we think about and go through in our actual real life as opposed to our academic life.

Not that both aren't important, but there can be two different kinds of philosophy. I think it's similar in math to maybe, how you can go into this world where it's actually really good to learn something. To learn logic and to learn all these arguments and it's almost like playing chess.

You're training your mind and I think math can do that too and you're really learning how to think in a way that's very productive. But that's a little different than the kind of philosophy I think that maybe we think of when we're young or that actually matters in a real world context where it's more about how do I get through life in a good way?

How do I deal with these feelings I'm struggling with?

Yeah, I mean, there's two levels and I would say, I certainly agree philosophy has this sort of mental scaffolding role in many aspects in life. I don't know if I, because I am, I'm a firm believer in sort of scaffolding your mind for with activities that are not the same activity as they are meant to be scaffolding for. And as an example, I played some video games that I sort of explicitly didn't like, or I didn't dislike, but I didn't enjoy per se, like the most. And I remember thinking, but these are going to push my mind into corners that are less explored and less developed.

And that's really fascinating, right? Because we learn patterns, don't we?

Exactly. Yeah. And I pushed myself to do. Certain tasks in certain video games, to have that I was naturally bad at so that with time, I became quite good at the video game.

And the video game, by the way, Starcraft two, in case anyone knows, as a real time strategy games and managing many units and multitasking. I was very bad at that mentally. I was very bad at multitasking. So, real time multitasking, and so I wanted to develop more. Channels of activity, simultaneous channels of activity, mostly because I wanted to improvise music and I wanted to keep several melodies in mind and things like that.

And of course I was training music simultaneously, but because I did play video games for fun, I felt, well, let's play a video game that maybe pushes into the direction of multitasking in real time and so on. So I started learning that game that I was very naturally bad at. And then with time, I became very good at the video game, but.

And I think it actually improved my, my multitasking. It is definitely correlated. I don't know how much causation is there, but, going back to the topic, I think, it makes a lot of sense to go on and explore philosophy and build on this, higher towers of thought, so that you have a better You have scaffolding for your life, basically. Another being has joined the conversation.

Yeah, actually, as you're talking, I'm thinking about something which I kind of know already about you a little bit, which is how you got into, to mathematics. And it wasn't easy for you either, right? Like at first, When you were a kid, you kind of hated math, right?

Is that true? Is that, do you, can you see the connection there between also wanting to expand your potentials?

Absolutely. Yes. Actually, it's a good, it's a good segue, because, this was very much the pattern for context, for those listening, when I was young. I was very uninterested by school mathematics, and I have to say it was a very arithmetic focused mathematics, doing all kinds of, addition and, long divisions and things like that.

The pedagogy of it was terrible, , long divisions and square roots were set as punishment homework, basically. If you didn't do some other homework like, geography or natural sciences homework, then you would Be assigned long divisions just for punishment, I mean, long division is boring.

It's an algorithm. There's no creativity involved. You might be, some people are entertained or in the meditative activity of just the following algorithm. I am personally not. So it didn't work for me. So for many years in, in primary high,

I was uncomfortable in most of the math lectures, and I was basically dreading the time when, oh yeah, I have to do math homework, it's so boring. It was a drag, in the best of cases, in the worst of cases, I hated it. Anyway, so when I got to high school and I discovered my love for science and physics and, through conversations with my father and getting some books, when he studied engineering and so on I realized, okay, so there's this way to understand the world that unveils, patterns and unveils, the sort of the mechanisms that are essential. So when I see a complex explosion of many parts flying around, I can actually isolate that if I track the position of this, Piece is actually just going to follow a parabola.

It's quite simple or, all these kinds of, ways to reduce the complexity of the world and understand them in a very pointed manner, in a very sort of precise manner. I fell in love with that. And, and obviously there was mathematics involved. Of course, the mathematics, the kind of mathematics that I was discovering at the time that worked for physics, where, things like calculus, things like vector geometry and vector algebra and things like that.

And in my ignorance, I was not aware that those topics were bundled together with the topics that I had done in primary school, like arithmetic and basic geometric shapes and things like that. And when I realized, I do remember the day when I thought, I must have been, I don't know, 13 or something, and I had been reading physics, elementary physics books, but with equations already for some time.

And I remember thinking, Okay, so, having been someone who stated that they hated mathematics for many years at that point, I came to the realization that, okay, wait. maybe mathematics is a much larger field that I realized that I got exposure to in primary school, and maybe actually, I love mathematics. It might be the fact that I have this fascination with what mathematics does for our understanding the world.

And it was pretty much a sort of a step function change. It was from thinking that I hated mathematics to realizing, wait, All these things that I'm loving about calculus and vector algebra and so on are mathematics, just the same as arithmetic was mathematics back in primary school. It was just the primary school forced mathematics into me and, I didn't want to, I didn't want to do boring algorithms and, but mathematics is much more than boring algorithms.

And I was doing much more creative problem solving at that time in sort of mechanics and basic physics. And then, yeah, it was basically one day that went from, Saying that I hated mathematics. I was a misguided opinion to a more proper opinion of actually saying, I love mathematics, but going back to your question, I was naturally bad at mathematics.

I was not very well, trained and predisposed. To symbolic computation, to logical reasoning. My, my logical intelligence, of course, is sufficient so that I can be, proficient in these things, but I wasn't naturally drawn to those things. I was not the one, solving puzzles or into riddles or into those kinds of things.

I was much more visual, artistic, much more intuitive. Sounds

like you are more interested in the big questions too, if you were thinking of the philosophy and the, which we don't often associate with math. It reminds me a little of Eugenie Chang, I think is her name. It talks about category theory and how, we think mathematics is so in a way that you're describing the way you thought of it when you were a kid, the way we all kind of often encounter it first in school, where it seems very dry and, it has to do with that training our mind thing, I guess, like what we were talking about, but then you can think of it abstractly too.

And it starts to relate to these bigger ideas. So it sounds like at some point you started to realize, Oh, That's a way, a tool that I could actually think about putting some scaffolding on these bigger, more like emergent, difficult, bigger things. Yeah.

Precisely. And just to to finally answer the question.

Yes. I decided to, when I had that realization, I thought, okay, let's get into mathematics. Let's do this. study mathematics, let's train my mind in mathematics. And I remember actually just setting homework to myself to do boring stuff. So I went from absolutely hating it, dreading it, to realizing actually I should set homework to myself.

And I spent summers just doing derivatives, by rules one by one.

Oh, wow. That's very disciplined of you. It's kind of, it's very similar to playing the video games that you hate.

Yeah, it's the same pattern very much. And so you, so yes,, it's a general pattern in me that I would spot a inability in some sense, some area in which my mind is not naturally drawn to, or I'm not immediately engaging with the phenomenon.

There are other things that are very engaging immediately, anything that has to do with like space navigation, shape, these kinds of things. I'm very intuitive and quick to it. I mean, my brain feels at home when I'm doing those things, even when there are difficult things, but there are other aspects that are very difficult to me and they don't feel like home.

They feel like alien. areas. So I always feel like a visitor in those areas. I mean, to this day, after, I don't know, 20 years of of mathematics in my life, learning and working and researching and so on, I still feel like an outsider. I don't feel like a, like I'm a mathematician. I have colleagues that, I had colleagues 10 years ago that I thought, Oh, these are mathematicians already.

I'm an outsider and, still today, I wouldn't say I am a mathematician, brand mathematician. I can go around with a mathematician's banner and just be happy with it. I think it's a good, it's a good descriptor. If you only have one word to assign to my profession, saying mathematician is the closest, probably in terms of work structure activity, work, ethos, and so on.

and the kind of activity I end up doing during the day. It's yeah, I'm a mathematician. That's what I'm doing with some computational research on the side. But but yeah, I still feel, I feel like an outsider and not to derail the conversation in that way, but I do think that this feeling of being an outsider is very much a an advantage for certain things.

Obviously I won't be the one to Solving the unsolved problems for millennia or the one that, gets into the deepest or the highest heights of theoretical constructions and contribute the thing that is going to sort of, round everything off. I think being an outsider allows me to see sort of paths that are less frequented or, ideas that have been underdeveloped or, ways of approaching problems that are more novel or, More original and things like that.

So,

so yeah, this is interesting. This insider outsider, right? That's another kind of either or dichotomy thing. And I can imagine someone who is like a pure mathematician or who only is kind of living in that realm of, that different realm of more actually living in the math might also feel like an outsider.

In a different way, maybe an insider in math, but an outsider in the kind of the worlds that you move more freely in. So it's kind of interesting how, I don't know, do you think we have to choose kind of, one or the other areas in which we're going to be a master or is there, it sounds like you've tried to do a lot of different things.

Have you encountered some struggles with trying to be in all these different worlds at once? Or is that just also kind of more a matter of this intuitive, natural thing? Natural what you're drawn

to, right? Well, that's a very hard question. That's the, yeah, I would say that's the core of doing this kind of thing.

I have colleagues who have done mathematics since they were basically a eight, nine years old, they got into some school competitions, then go on to some Olympics, and then go on some, like the International Olympiad, all that kind of stuff, and then go on to do a mathematics degree, get a PhD, get a postdoc, and I have colleagues that have gone all the way, and every single step of the way, they felt comfortable that this is their tribe.

This is their country in some sense, their intellectual country. And they are very much aligned with the culture, the problems that they want to tackle. And they are doing very difficult things that try things that are trying to solve are very technically difficult. And so I can certainly see the appeal in that.

And I and Even personally, and I think it's obviously very important that people do this because that's how you get really deep into topics and you get really progress in the end I think progress most progress is done when people going in this very directed way. But at the same time I think there's there's certain almost personality types that I think fit better in, in being generalists.

It's almost like an ecology of research, right? I mean, you have specialists and you have generalists. And if you have a, an overabundance of specialists, then nobody understands each other. And we're basically all walking in divergent directions and we don't end up really making any progress other than the people Personal self development exploration sort of experience for each individual.

And if everyone is a generalist, we don't really get any depth or any nuance and any detail in the explorations. So it really has to be an ecological balance of specialists and generalists and all kinds of intersectional interests between the different researchers. So I want to, at least this is the, the narrative I tell myself to sleep at night, I guess, but I like to think that having generalists is is an important ecological element of any research environment or more generally, any intellectual environment.

And so that's why you always would have figures that are not. absolute experts on any one particular topic, but have spread out. I would say though this this is not to say that you need figures. So in a way you sort of specialize in being a generalist and it's sounds a bit paradoxical with the terminology, but that's just as an imitation of the language, not of the ideas.

And I would say that you specialize in being a generalist in the way that you could be an expert, a specialist. But you choose not to in a way and this is certainly my experience, my personal experience has been, I could have been a physicist specialist, like a theoretical physics specialist or a geometric mechanics, geometric fundamental physics with, different geometry, this kind of stuff.

Specialist. And during my PhD that was kind of what I was, and, doing my research on that. And I published a couple of papers on that and, I did that kind of work. But I deliberately chose not to go down that path because I felt that it led to a life that was very constrained in the kind of intellectual realm that I was going to explore.

It was very much in line with the sort of ongoing, in my opinion, the ongoing sort of not so productive dynamics in academia, which is, you have to over specialize so that you produce more papers, more incremental papers, and you can have, a longer list in your CV and more chance for higher impact and all these kinds of things.

And I made a very personal conscious choice of, I don't want to play this game. I want to make something happen. I want to do research somehow, because I was still, I thought I was young and I had, valuable ideas to some degree, so I wanted to still produce research, but I didn't want to play the academic game.

I didn't see myself as just becoming a professor, although I love teaching as an activity, but I didn't see myself become a professor after all this game that you have to play and all the, in the academic world. So it's not that I discount an academic like profile for my professional future, but I certainly rejected the model.

that I just play along. I do post ops where I just focus on paper after paper. They're all kind of piecemeal contributions. There's nothing, there's no grand narrative being built. There's no one fundamental problem that I think is necessary to be solved, but it would probably take years. And then I sort of settle.

And then maybe when I'm in my late forties, I find some time after I had family or whatever that I did that didn't seem I felt like I have the energy now. You only live once. So. I have to do it now. So it was a joint personal choice and a more intellectual sort of inclination of mine to be multidisciplinary and to be exploring all kinds of questions.

And so yeah, it's it, but it's a very difficult balance. Yeah. Did

you worry about, I mean, because this. I definitely know what you're talking about and there is this kind of point system to academia in a way it is like a game and I think that's a good analogy, even if it's not a game, and for you, you kind of have to participate in some kind of a game in order to do traditional things like, build your career get paid build your reputation and Did you worry about rejecting that?

Because there's a reason why that is such a solidified trajectory. And a lot of people don't really want to take it, but they're afraid not to take it. Were you ever worried about that?

I guess worried. This is a funny question because a friend of mine was just asking about that yesterday. He asked them something about, what do you normally feel during the day?

And, they mentioned worry and anxiety is something that they felt. So, but it's funny because I don't think I worry that often. I don't think that I'm lucky that I don't get that mental state of worry. I think I'm more of a, I'm a very optimistic person in general. I think I have a very positive outlook on what things I do.

So when things go bad, because they do go bad, I was very lucky in my life. I was, there, there are many instances where. outcomes could have been a couple of ways and it went in the most positive one for me. But there have been moments of failure, absolutely, and not getting things that I wanted and, and the main plan failing and things like that.

And I think my personality is so that, I just take that. Oh, this is the world I live in. I have to move forward. And so when it came to the decision to I wouldn't say leave academia. That's not, I didn't decide to leave academia per se, like other people say, okay, I'm going to colleagues of mine that have gone to the corporate world or, to financial industry or whatever.

I didn't make that kind of rejection where I said, okay, this is going to be a Parallel world that lives besides me and I'm gonna be in this world of whatever industry. Or other things. That's not what I thought. What I thought is, okay, there are valuable things in the world that I feel like I can con I can still participate in.

Meaning that parts of academia certainly, or I would say even the majority of aca, what academia does is very valuable. The companies and institutes and independent nonprofits and all these kinds of contexts where. very important and interesting human intellectual development is going on in the present.

And I thought, I think I am in the most productive years of my life. I am kind of fully trained, fully formed as a sort of young adult, mind, whatever. And I felt, well, if I'm going to contribute anything of value, it's going to be now it's going to be in the next few years. Right. So, I just basically decided I don't want to be busy with the, with this with this game of if I have this topic and then I can do two papers, if I have this other topic, I have two more papers.

I've decided instead of investing time into that, I'm going to invest time in setting up a society at this nonprofit, or I'm going to, or I'm going to do the research I think I should be doing, but that's going to lead to maybe just. one paper a year or maybe two papers a year instead of the six or seven that some of my colleagues are writing and and This eventually I think I can say safely today, after having had a couple of the main papers accepted in the research, that this is working out in some sense.

I mean, I did find some unconventional context to carry on work and to get paid and to survive, because at the end of the day, you have to make a living. And I am also setting up my own means to do that in sort of like in, in this sort of entrepreneurial attitude. But so to answer your question, was I worried to drop that?

I would say the worry, if I was worried, worried at any, for a few seconds that turned very quickly into, these are all the things I'm going to proactively do. To just. And be, I mean, ready to, because what I, the decision did feel more than dropping something that is conventional and well established, which it is.

It felt more like. There's a path over there that is hard to climb because it's certainly a hard game to play, the academic game, but it's very well trodden. I can see the, I can see the trail clearly leading to a summit. I can, it's hard. It's going to steep. Many people are climbing it and I'm going to have to raise other people, but it's very clear where I'm going.

The other was, there's this forest here. There's no path, but you know, what I see in the distance is a much more beautiful landscape, right? It's much broader landscape. And so my decision was. Okay, I could go there. It will be fine. Get a nice view from the top of that hill. But I can see this beautiful valley with, higher summits and, beautiful, waterfalls and things like that.

And, but there's a forest in front of me and I have to just get into the forest and start, like doing some complicated navigation to make it work. So I am in the forest right now. I feel like I am in the forest and I'm navigating. And I think this fits my personality much better, like in a very holistic sense.

In life, I, when I went hiking, I liked going to the mountains around my hometown here with my father when I was younger. When I was a kid, I was with him, in the path and the trail and everything. It's kind of safe and predictable. When I was old enough to go on my own. I always wanted, through, through the hills and, with my sister climbing through the cliffs and, all sort of, free cross, cross country kind of,

exploration.

So, yeah, it's interesting because this gets to the love part kind of in a way, or However, we want to, because that can be a real motivator, right? And that can, I mean, if we zoom out and think, okay what is this life we're building these paths or we're following other paths or what is it really all about?

It sounds like you are more connected to that. Okay. I'm feeling a lot of motivation. Love is a big word, but love of wisdom, even this is kind of what I feel drawn to. It's almost like you had a restlessness, a lot of energy you needed to do something with and trying to put it into those traditional forms and paths.

Of course, you could do it, but something in you, let's call it love. Yeah.

I like the word. Yeah, if I may I'm very comfortable calling it love because I think it's a very good, I mean, maybe we can get into the technicalities of definitions of, is it love for people?

Can you actually love something that's not a human being? Whatever. But I would say at least as an analogy, it works really well because It's something that is very irrational in a way. It just, it's inside of me somehow. It's an inclination. I don't decide it. I certainly, I sort of channel where it goes, but I don't really decide that it is there in the first place.

And it is, it was a very conscious choice in the way that you described. I actually remember, I could input this energy, this love. For wisdom, this kind of going after philosophy in the etymological sense in academia. And I was already in academia, I had a postdoc position that could have been extended and it was a sort of research teaching position that would naturally turn into sort of a, whatever, junior professor position, you were on

the track if you

wanted. I was definitely on the track and and I could have kept going and it was, and I was fulfilled by this. And I was doing research and I was teaching and I loved both. So it was great. But when he said this was around the time. I mean, the context is actually relevant here.

This was around the time when COVID hit. So I was lucky to have this job during COVID. So I had some stability during the pandemic and the lockdown and all that stuff. But. I did think during those years, the couple of years of the intense sort of pandemic restrictions I did think, okay, so the world is much larger than this pocket of academia that I found myself in and that is sort of my wedge, wedge myself in And I thought, I can certainly see the value I can contributing in that pocket.

And I was already sort of seeing it with a very positive reviews from and feedback from students and, everyone praising my teaching and, my research sort of picking up speed. And so it was a. It was a positive environment. Okay, granted my research group wasn't the best and the leader of the group was a bit of a, academic asshole, if I may say that kind of term.

So I'm not going to ask who it was, but yeah. I wouldn't say any names, but but it was, I mean, it wasn't that bad. It was just that, in terms of the style

of those environments can be really

tough. Exactly. So it wasn't on me. It wasn't that tough, but it was not the greatest, but nonetheless, I was in a positive environment.

In a net positive environment, like in a life situation, right? And so, but I was very restless, as you say, because I thought, okay, so I have all these ideas, all these energy to contribute. And it wasn't like I am the sort of egotistical sense. I have this idea. I want this to happen, and I won't have it any other way.

It was more in the sense of, I feel like I have value to contribute to things that I find otherwise communally valuable, so that everyone can benefit. Thank you very much. And I felt that by being a professor or in a professorial position in a university, I could do very little I could very, just influence a few students motivate students, and that was rewarding I'm fine.

But I felt like we are living in a very interesting era in civilization in the world right like we have all this emerging technology we are in some kind of probably I mean who knows, we won't be there to see it but we're probably. Right. This era will be the era where many things are sort of defined for the first time right we're transitioning to this massive information technology era,

definitely a big transition happening.

Yeah, I mean I guess there always is but yeah it's hard to see completely but I see what you

mean yeah right and so I felt like by being an academic in pure mathematics in theoretical physics by the way it works. I didn't have to really engage with most of the interesting systems of society nowadays.

And by that I mean, I didn't have, it was enough for me to quietly type away my paper and to go to a lecture and give a blackboard lecture.

So again, I think we have this, you wanted to challenge yourself in a way, the same with the playing the weird video games, going into the stuff that was hard for you.

That, It's almost like you didn't want to take the route that was comfortable or but I have to say a lot of people I've talked to they just to kind of make a little side note about teaching actually teachers do change lives for sure you know this right like just one or two little comments from A teacher can put a lot of people I've talked to who are very successful right now They all attribute it back to one professor or one teacher So I just need to put that out there that is actually you said you might not change the world I think it's more specific for you like your trajectory, but sure some people's trajectory being that teacher You are definitely changing lives, but that gets me to your restlessness and your you're not wanting to be comfortable, right?

So you'd kind of found this comfortable world and it's almost like immediately you started looking for where's your challenge You

That's right. I mean, and just to go briefly go back to the teacher point. I absolutely agree. I mean, and I love teaching. I've had a very natural inclination towards sort of education and explaining sharing knowledge from a very young age.

I mean, just as an anecdote, when I was, I think, six years old or something in primary school. One of the games that I played with my friends in playground time was I brought several copies of the same dinosaur visual atlas and I would go over, let's go to page three and let's name the dinosaurs on the picture and things like that.

So it's a very strong inclination for a young age to like share knowledge and yeah.

And you're still teaching even, I mean, it's not like you gave up teaching. That's still

part of your life. Absolutely. It's part of my life. Absolutely. Yes. So the restlessness this is funny because, and this conversation is actually going to prove a little bit. self introspective and therapeutic almost to a degree because for many years during my student years and PhD in Edinburgh and, in mathematical physics. And I actually had this view of life, which came from early childhood, even from my parents and the context.

I mean, I was born a child of the welfare state

That is very similar to what we have today. I haven't seen a lot of progress happening from my childhood to my adulthood, right? There's

no match. Economic scaffolding. Economics

and. Social. Okay. Exactly. So the contrast is my parents generation here in Spain, they went from, the fascist transition to the, to democracy, economic development, the European union, all these kinds of things, right?

The U. S. is our regularities there. Exactly. So there was a much more clear gradient of society. And they felt very responsible because they indeed were the ones making that, in, in aggregate, they were the ones making that, that change happen. And this is certainly something that has changed radically in my generation.

We. We didn't feel the protagonist that we had to enact some kind of development or some kind of transition to anything, so kind of development. So it was it certainly has affected, I think has affected a lot of people psychologically, although this is an entirely different conversation. But in a personal, in a personal at a personal level, when I was a kid and a, teenager and so on, I always saw life as.

A way to make yourself a stable environment where you can just basically let systems running and you just live away in some sense, right? And this has only been in the, in recent years that I fully realized that this is not the case, or at least for me, it's not going to be the case. Because, and I think it's a good fiction to have in mind, because obviously if you work towards.

Making yourself in building yourself in a stable environment where you can sort of, sustainably continue to do activities that you want to do. That's actually a worthy goal. And it's a very difficult thing to set up. So the path to get there is very valuable is something useful. But I realized that, and this is probably completely obvious to many people, especially people in behavioral sciences or psychology and things like that.

I mean, When you get to a reward or you get to a state of completion, you lose the drive and therefore after a very short while, you're demotivated, right, or depressed. And I have been depressed several times during my life, precisely because of that dynamic, because I anticipated, even for years, getting to a certain position, realizing some patterns in my life, some conditions that I thought would be good.

And we're good when they need to happen. After a short while. being depressed, basically.

I think that's really interesting. Let's dig at that a little bit, because there's a lot there. I think a lot of people feel that way, especially if you're going to go into something like academia, because there is that trajectory that we talked about and you do, there's so much that you have to do in, just in terms of the work that's involved in the classes and getting the grades, and you do kind of have this idea that you're trying to get somewhere and sometimes you just wake up and you're there and it's not at all.

You, for the first time, you're what was all that work? And what is this that, there's a weird jolt, I think that people experience and it does, it can be depression or it can be, I don't know, then you start some other thing. You, maybe you start your family or there's a lot of ways we try to deal with that without, we don't really talk about it though.

Yeah. But yeah, so I'm kind of hearing you say maybe that was part of this thing that happened in COVID too, that you'd gotten, not a plateau, but you'd sort of, you'd kind of won the game. You had the points or you knew now how to play the game and you wanted to switch games or something.

Yeah that, that's a good, that's a good description.

And maybe a a relevant anecdote in that is where which ties to my childhood story. If I might give the context briefly. So I wanted, as I mentioned earlier, I wanted to, I would, if you'd asked my 12 year old self, I would have said, I want to be a theoretical physicist. Obviously I didn't know properly what a theoretical physicist was at the time.

I was probably not that far off because I ended up becoming a theoretical physicist PhD after a while. So, so I did want to go there. I did know that. I was interested in everything. I wanted this going back to this philosophy, love for knowledge. It really meant love for understanding. I mean, the word I like to use is understanding. Because I, knowledge, I think is a, to me, sounds like a very grand word. And I personally like to use understanding because that's certainly, I mean, that's a subjective experience I feel.

And so it is very traceable. It's very operable, right? So anyway I definitely experienced understanding in some crucial moments in my life when I was in my formative years and I, yeah, I aimed, I want to be, I want to be a mathematical physicist.

I want to understand the world in a formal way. And I, in this sort of fundamental approach and the kind of, Influences, although maybe not so direct influences, but the kind of the context that I was experiencing at the time was reading sort of, pop science books by Stephen Hawking

I was just about to ask, did you have a vision, like a mentor in mind when you, cause I know you're into, you were doing experiments when you were a kid already, so. I guess Stephen Hawking kind of. Yeah. Is that

I could you could point it. Yes. So you could. So I would say that the biggest influence the biggest of human singular individual influence was my father because I was I remember the day I was with him in the car.

It was driving and I was in the copilot seat and I. I was just asking a lot of questions. I was not like young kid, lots of questions. I was already like, 11 years old or something. And I was asking, all kinds of questions about if clouds are made of water, where, where does it go?

How does it flow? How tight can a seal be to hold what these kinds of, my father's a hydraulics engineer. So, there's a lot of questions about water and things that anyway, but a lot of questions in general about the world around me. And, at that time I thought I wanted to be a paleontologist and study dinosaurs sort of, because my parents had built the narrative in my head that, if you love dinosaurs, which I did, I do then you can pursue this as a career if you are serious enough about it.

Right. So you were in the

Jurassic Park dream. Absolutely.

Absolutely. I mean, Jurassic Park was my favorite movie for me.

What a transformative movie. But anyway.

Yeah. Yeah. So, so my father then, so after asking so many questions, I was left a little bit, like pensive thinking, ah, so if I love dinosaurs, And then I pursue paleontology.

If I love all these kinds of questions, random, to me seeming seemingly random questions, I was asking what do I pursue? And my father was maybe you should pursue physics. And that's the first time I heard the word physics as a word in Spanish. And my father said, and I was like, Okay, what's that?

And so I got curious. I got a little book, this visual atlas with some equations, have no idea about equations at that time, obviously, but it became very intriguing. And then I started like sort of forcing equations into my mind just by reading the context and my father explaining that's a variable, you can assume any numerical value.

And then very quickly, observing a few months, I started the idea that, oh, right. So there's, there is deep. knowledge here. There's deep patterns being revealed here. And because I could relate it to daily life, I could see, the things moving around me and I could look at Newton's equations and I could see the connection, in a very better sense.

So my father was a very big point of influence, but I would say that after

that, I have to stop you there because this is interesting with the love too, right? And that, and the understanding that it's your father who it sounds like kind of was, showing you how to look at the world as a magical place, right?

And there's all these questions and things to observe. A lot of kids that don't, we stop observing the world when we're really little, we do. But then you kind of learn, oh, that's, everyone tells you that's what that is and that's what that is. And it's not this questioning and, constant observation and what could that be?

And it sounds like your dad was sort of instilling that and also your quest for understanding. Was it tied to your love of your father and wanting, wanting to engage with him or so? Okay. So

that's actually a relevant question. So, so there's the philosophy side of the question and the love side of the question, which is very appropriate for this podcast.

So I would say my father, what my father did was. And he was, in my opinion, the best way he could have been about this was to show and to and to offer, but he never mentored me. This is an important thing. He never mentored me. He never went with me and sat me down. Okay, let you do this.

You I asked him a lot of questions. I asked him for help. It always felt like cheating to ask him for help because obviously he had trained in engineering. I had an idea of what that meant. I had an idea that he spent years in university studying these books that I could see at home that are actually just behind me now.

So, so all the, all that I could see and I asking him to help me and train me felt like cheating. And this was a feeling that I just felt personally. But my father was amazing at. offering me. He was like, so here's a book about mechanics. If you want to learn about this and that, there's the concept.

He never forced me to do anything. He never like strongly, suggested one thing or the other. It was more of me. I have to say since I'm the kind of the kind of mentality that. when you, when I switch into a direction, I might need an influence for that. And I always attribute context and other people's influence to all the kind of change in direction and so on.

But once I'm set in a direction, I'm very much sort of a, all steam ahead. I just run right with it. So, so in that sense, that's, that was the sort of the role of my father there. Now, when it comes to expressing my love for my father through this I would say that what I had for my father was mostly sort of admiration at that point.

And then, and as I said, like seeing someone, I mean, my father, my mother, both were extremely loving. And I think I, I always like to say that, love has not played that big of a role, love for humans. I mean, it has not been, has not played that big of a role in life in my adulthood because I was given so much love as a kid from my parents,

I have the reservoir state or something that

yeah, it's like my reservoirs are all the way up from love from childhood.

And it's, it can deplete a little doesn't make a difference in so much. So they were loving. We were a loving family. I had two younger sisters. It was a very loving environment. Everything's great. Still is to this day. It's a wonderful family. But. But yes this context was certainly the main interaction I had with my father.

It's just me sitting with him, usually in the car or in some context, and just asking questions. Lots of questions. Asking questions. Asking questions. And pointedly, he would explain something to me because I basically asked him.

You asked so much. Did that just come from you? Or was he inquisitive? I guess, of course.

It

was just me. It was. I mean. So

that was just you wanted to understand the world. You don't know where that came from. Maybe.

No, I think it was absolutely I mean, I cannot find an influence for that. I mean, I think I'm just very predisposed to this because I

didn't have a Your senses are sort of turned on the world in a way, in a

Yeah, I might, I mean, this is fractalizing as we expected.

The conversations are sort of fractalized in interesting ways. But I do think that my personality has this outwards. Orientation. So I was talking to a friend of mine who actually was in the summer school where we met each other ago. Who was talking about, okay, so how do you work, psychologically how do you feel like you contribute to your community and friends around your family around you.

And I, discussing different. Spectrum of autism, a spectrum of re how you deal with relationships and, drama people and so on. Yeah. I said, well, it's interesting that I don't have a very directed social drive, meaning I don't, I'm not the kind of person to seek sort of just social environments for the sake of social engagement.

. However, I have a very strong intuition to organize social as I mean, I've organized Yeah, that's what you do and so on, so, so. And for a long time, I was a little bit confused about this sort of the nature of me not being very socially directed in a way, but being quite driven to set up social gatherings and set up sort of an organized sort of situations where social interaction happens.

And I think I. That seems

like a dichotomy, but it seems

like a, I think it's not so much a dichotomy. Or maybe it is actually a traditional

dichotomy. I don't think it is, but it can seem like it, right? Like you're trying to, it seems two parts don't fit together, like they're opposites or something within.

Yes. So, so I think it's a fitting example of a theme that I think you mentioned you'd like to highlight with this podcast, which is, having that formulation in mind. Okay. So I am, it is true. It's not just a formulation. It's not just language. It is true that I am not very socially driven.

It's true that, I love meeting my friends and close family and everything, but I don't seek social. Social company, just for the sake of social company. Yeah,

I, I really identify with that. Believe me, I know what you mean. Yes. Yes. So, so, and yet also I hear what you're saying, cause it's actually also one of the kind of themes of your life in a weird way.

Social. So it does seem paradoxical as maybe

the best. And I would say it really isn't in, in the following sense. So, And I came up with this narrative. I mean, it's going to sound scientific. It's really unfounded, but the narrative is, has scientific sounds. So, so the narrative is basically if you want to select a sort of tribal structure.

And you have, you must imagine that, humans have a lot of interspecies variation, right? Like we have very different heights, strengths hair colors, skin colors, all these kinds of things, right? So

Within certain parameters, of

course. Certain parameters yeah, of course. Within

some bounds.

I mean, just being human, you already have a lot in common, but I, yes, I know. Of course. There's a lot of

Yeah, but there's a lot of variation, right? And we have also like sexual variations. We have like age variations, like individuals have different roles in a community,

sensory variations, how we, exactly.

So, so if you think of that, if you think of a tribal structure more in the, the ancient history history eras, like if you think of the tribal unit as something that is. Selected for and it's basically doing some adaptation navigation to, to evolution. You need, it's actually important that you have this separations of individuals because you need, I mean, you need a core of of a tribe that is very socially driven, that, is very, driven by affection, driven by social dynamics that cares about who others are thinking, cares about how others are feeling and, looks.

look after each other, all these kinds of things. You need also people that look outwards of the tribe and they're essentially sort of like looking out and they are not really thinking about what's inside the tribe, other than the tribe as a whole concept, right? Like they have the concept of the tribe as something that needs to, you Function.

But these are the planners. These are the hunter gatherers actually go out and hunt and gather and so on. It's this kind of I mean, it's a very reductive story. It's not, as I said, it sounds like scientific, but it really

is. No, I think it's wonderful. And weirdly, it reminds me of category theory in the way you're kind of looking at patterns of patterns rather than like being.

Just in the pattern somehow.

Sure. Yeah, exactly. And and I think what I, what happens to me is that, if you give me a network of humans and you give me a network of people I would be drawn to engage with that. If you give me a system of human beings doing things and interacting with each other and organizing to do some things in the world, I am engaged with that.

I have a natural drive to, to work towards that. But if you give me a single individual. with whom I am not in the process of building towards those things, or I'm not, I don't know, engaged in some other kind of dynamic, like romantic or very close friendship or something, I'm going to be very uninterested.

My, my sort of interest drops down and I feel like, okay, this is fine, but I could be doing better things with my time in

this context. The pairwise interaction is not, Yeah,

you could put it that way. Yes. The one link interaction is certainly less. I mean, and this is just judging from my history.

It's not even my preference today or the active decision that I'm making today, but just looking at the pattern of my life, you can see how all my friendships have been built around activities. And not just they happen to be around activities, but they hit around the activities themselves.

And I have, I've had a drive to organize communities and organize sort of complex activities that involve coordination and things like that. And I'm always very comfortable with, the complexities of all the details and things like that. But I'm not so keen on. Just being friends with everyone and, getting to know how everyone feels at a given point.

So, I need the important information about that, are your feelings impeding you to be this or that or, and, make sure that you're feeling okay so that everyone, everything can process, everyone can feel okay. That's important to me. But beyond that, everything is kind of like unnecessary complexity that that is not that I find worse or uninteresting in a more philosophical sense, but In practice, it just drops down in interest and it goes

to a backdrop.

Oh, this is really fascinating. I mean, we have to go back to the Stephen Auken fractal at some point. Let's stay on this fractal for a minute because that's interesting. It makes me think of this Gregory Bateson quote, which I like a lot, which is, it takes two to know one. I wonder what you think about that because it sounds the one there could be the group, but also it's like you can't just with two people kind of know because you're more turned towards the space that's holding those two.

That's what you're wanting to be interested in. So there's something very interesting in the way you described it and I can see it kind of In the, just knowing you're very, not very long, but this pattern of what's motivating you is always some kind of larger category or something that you need a lot of input.

So, I don't know. What do you think? That it takes two to know one. What is that? Oh

I completely agree with that statement in general. I mean, you can interpret it several ways. It takes to know one I can think of as the notion. You always

have three sort of, sorry, but yeah, go ahead. Yeah.

Yeah.

No. I mean, as a notion of self that he wouldn't, I don't think it may, if it makes a lot of sense to, or not to get completely lost in the metaphysics and the epistemology conversation here, but but you know, the notion of self, I think I've always understood as a.

As a mirror phenomenon in a community. So, and until there's a second one, like there's two, you can really know that there's one inside of you of the two, right? That's

really interesting. And even bigger than that, maybe is that you're only going to see one particular reflection. So really you need two to get even a slightly accurate vision of yourself to other.

Yeah. You will see your reflection, even if it's an actual virtual. You will be at two, right? Like it will be there's a one on the reflection, but anyway. So, maybe fractalizing all the way back, cause I think we got into why I ended up liking and

discomfort and mentors and how do we link on

those because yeah, I can reconstruct back.

So basically we were from my father's influence and then what he did and how I eventually moved on forward and so on so going back to the, to that story After my father basically opened the door and said, Here's this path, you could follow this, there's such thing called physics and so on.

I basically just ran with it, I asked for a lot of things, a lot, obviously, like I got everything from my parents until I went to university and so on. So, so I got books, I got a blackboard in my room, I got all the, and I got,

Yeah, that's that comfortable, blessed kind of zone you

were describing.

Yeah. Yeah. So, so one of the books that perhaps was most popular at the time that was coming out are these sort of second wave of Stephen Hawking books about, the universe in a nutshell.

And the black hole and all

that. Oh, okay. Yeah. Yeah. The ones that, because the brief history of time, that's in the, I think eighties, a long time ago.

Yeah. I mean, that, that was popular, of course, still, but there was this this wave of pop side physics books about string theory and quantum physics. Yeah. The elegant universe, all these kinds of books were coming out. So I didn't read actually probably didn't finish any of those books from beginning to end, because those are not really books to read from beginning to end in some sense.

But I definitely read a lot of. And I read some physicists biographies and things like that and know the history of physics a little bit, 20th century physics and things like that, like Einstein and, fathers of quantum mechanics and things like that. So, but Stephen Hawking was obviously very striking very prominent figure because of his condition and because of his contributions, the ideas are also quite interesting and so on.

And so, I read his books and I knew of him and I saw him in documentaries. I mean, also, documentaries were a big thing at the time, yeah, channel or whatever. And so I, by the time I was reading those books, by the time I was watching those documentaries I was already on the path. I had been for a couple of years already determined to, okay, I'm going to build towards this.

I'm going to learn mathematics, which is comes very Difficult to me and not very natural. I'm gonna do go through all the struggle to go to the best places to do the physics to basically, so I'm from a relatively small town in Spain, and I moved to a bigger time to do physics in university. I basically kept on working on that dream.

And this goes back to our earliest topic of, when the struggle and building towards something and so on. So this was a very long struggle, I would say, was almost like a. 10 year long struggle from when I was 15, maybe eight year long or something. It was very long. And then eventually I, I worked really hard.

They got my very high marks in university or whatever. And I got a scholarship to go to Cambridge full funded and study in, in the, the mathematics department in Cambridge and do the. Masters that is the gold standard for so that on this side of the Atlantic in Europe is the gold standards for mathematical physics.

Oh yeah, you won the game in a way. Yeah, so,

which was exactly which was in the department where Stephen Hawking was physically. He was there. So, I remember very clearly, today, I was sitting at a lecture by. The, by Stephen Hawking's student PhD student former PhD student, who's been a professor already at the university.

And I was sitting at the back, just having my lunch so that, I'm not in the first row, just being sat there, just sort of quietly eating sandwich or something at the back. And then at the beginning of the talk door opens and in comes Stephen with his chair and everything, and just sits next to me, just listening to the lecture.

He sat beside you? Yeah, he sat beside me because I was in the last row on my own and he couldn't go down the stairs for the chair And I remember thinking, I had seen a couple of times sort of just moving around in the department and it was always Oh, he's there.

He's just here. It's not a celebrity

moment. It's just trajectories connecting. That's a powerful moment, right? Yeah,

absolutely. And then, at that moment I was sitting there and thinking, so I am listening to the same lecture he's listening to. And it's okay, so I'm not listening to a lecture by him, or, I, we are both listening to same lecture on black holes or whatever it was.

And so in that moment, I realized, okay, so this is the place, this is the place that, I was imagining when I was a kid, how would it be like, would it be like, and, to go to Cambridge in that mentality, coming from someone who, literally said hated mathematics to where, Newton was and, where all these very deep history of mathematics in Europe was to me, it was very striking.

So what happened to me there was that I kind of lost my love for the field of theoretical physics in

a way. Oh, that seems so, Like the opposite of what

yeah, it would seem that it would be naturally sort of like the success moment of I made it here. But I think that I think this anecdote tells you a lot about my restlessness, which is which was the original question that I was trying to know.

It's a great example of that. Yeah. Winning the game arriving and then

yeah, exactly. And because I think I could imagine. Telling people and I told people and they everyone think oh you went to Cambridge and you met Stephen Hawking and you They all talk about his great success and so on but obviously to me I knew the path and I knew that getting there That's literally just the logistics of doing the science.

I was interested in the science in the first place. I didn't want the prestige or the mystique of going to this millennia old university with all these traditions and all this mystique and all this history and all the geniuses that went through there and so on. That to me is the consequence of the communal activity of science.

That's not the point. And to a lot of people, it was the point to a degree. And many colleagues of mine left academia saying I was here for the wrong reasons. I was here for the prestige. I never really cared when I thought about it twice, never really cared about black holes or about, I had colleagues that basically quit their PhDs because of this kind of inertia to the allure of prestige and sort of like intellectual ability and so on.

And to me, I was always there. I was there very much aware of this aspect of academia, because I had built this narrative in me, I had built this sort of struggle to go from being a not naturally talented person in mathematics to through sheer effort go get a scholarship to go to Cambridge and, do these things, which I managed to do.

But when I was there, I realized Okay, so now we're here to do the work. We're now to, we have to do the thing that I wanted to do in the beginning, which before I even knew about Newton and Cambridge and all these kind of historical components and social all the prestigial, the reputation of the different universities and so on, before I got into any of that, I had for a few years already been enthralled by physics and the concepts that forces and derivative functions and all those things.

So to me the use of it the actual substance of science and philosophy in a broader sense was the driving force. So when I go to a place and I saw that there was so much noise around it and the science itself, was dubious at times, because I was disagreeing with the way many students were approaching physics because they were essentially taking it kind of dogmatically and then make it sense of it later.

I mean, I didn't really agree with this sort of approach. So that's why I kind of fell out of love with the field, with the social manifestation of theoretical physics, at least in that context. And at least for that time, because I thought that the substance of it, the core of it that originally motivated me when I was essentially a kid, was that Was not so much the driving force where I was.

And so

I thought, Oh, we have to stop here for a second because this is really rich. And this is, I think, an experience that people have in many different contexts where, Sure. You're so passionate and excited and, Motivated to it can either be about the people as it sounds like it was or to be a part of some social group because that is a motivation, right?

I mean, we're all human and like we have mentors or people that we look up to and sometimes without even thinking we just want to be in their presence or be like them. But then, of course, once you do a lot of introspection, like it sounds like you did, it's it becomes more about solving these problems and

there's this. Earnestness about it in this like in this belief that you can do it and that those people actually have some kind of answer and I'm speaking more from my own when you get into those environments and you realize, Oh, maybe these people don't have the answer or even it sounds like you saw a little bit, not with Hawking, but maybe with others around where you start to go, Oh they're kind of acting or pretending, or there's something going on here that feels not Like this earnest, earthy thing that I thought this was.

It can be so disappointing.

Oh yeah, definitely. And I think in my case the dynamic that you describe of wanting to be in a group and maybe being surrounded by certain kinds of people. And so, the story that I drew in my childhood is to illustrate that it is more for me the meeting up your heroes and, your role models and things like that, that came second in a way, because I was initially very driven by the, Substance of it.

I was absolutely excited to

I don't know. That's how you discovered all those people in the first place. It's

not like exactly. I mean, I mean, exactly. I mean, I discovered them as a, in a way it's almost like how I make friends. And I said earlier, I make friends by an activity like, I was absolutely obsessed already how you compute the time that that a perturbation in a hanging rope that travels to the ground, in a long hanging rope, because I started outside my grandmother's apartment one day is like I was wiggling it and I was seeing the perturbation sort of go down.

I thought, huh. I know that the perturbation speed on the rope depends on the tension, but of course because the rope is hanging at different heights, the tension is different because at the very bottom there's nothing and the very top there's all the weight of the rope. And so I thought, so how does that affect the speed, and I could see I could measure that the perturbation takes three seconds to get to the ground from a fifth floor or something.

So I wanted to like compute and I realized that there was something very interesting to do that. I was absolutely enthralled by these things. Like intuitively, there was no social drive. It was not socially cool. It was no I didn't care if Stephen Hawking was regarded as a genius. I thought I was very dumb.

I still do. And I never had any pretensions to climb any social ladder or anything like that with this. It was very, Intrinsic interest that I'm directly engaged with the

thing. I'm glad you gave that example because it shows that you really were caught up in that because it can sound almost like, you hear all these stories of genius people and they were trying to solve these things when they were kids.

Right. But there really is something about when you're a kid, you're just, you're engrossed in what you're engrossed in. Right. And that's what you were just naturally, that was the thing.

Exactly. Exactly. And I didn't lose that. I didn't, throughout my life, I haven't lost that, sort of, a feeling of being absolutely engaged and in love with, that's why I said that the in love analogy is strong, because I haven't lost that, I don't think, and in a way, that's what made the situation in Cambridge, for example, as a pragmatic example in my life, so, so, How to say so conflicting and so sort of like mixed feelings about it and so on, because I was there, I made it by all metrics, by all the standards that I could relate to my friends or to my family.

It was a great success. My family came, they saw the graduation ceremonies, all these like millennial old traditions in Latin and all this kind of like paraphernalia. Yeah, it's the time. Yeah. And I was there and it's, yeah, I was very happy. I felt happy because I felt like I accomplished something difficult.

But you know, when I went down to my intellectual, back room, just back to my childhood, to my actual intellectual interest, I saw them more far and far away. And I was like, okay, this is not working. And this is not, so I moved

on. That's a hard thing. That's a lonely place that, that weird, that

feeling.

Yeah. And then I think the general sort of direction of of The general direction of the of the path was I want to become more like my child self. I want to be that scientist with my more advanced training now, my more advanced mind in a way. But I want to go back to that. So I did a PhD in pure mathematics as almost as a rebellion towards physics in a sense that I said, okay, I don't want to think about this particular tradition of theoretical physics.

I want to do something in pure mathematics. So I did. Differential geometry, which arguably is very adjacent to theoretical physics, but it was really in the pure mathematics sense. And then after many years I, during the PhD, I eventually sort of reconciled myself and said, okay, now we are far away enough from, all the context that I can.

basically remake myself as an intellectual. And this is one when I became myself today where I decided to be more explicitly multidisciplinary, although still focused on the questions that I think are valuable and, no longer seeing disciplinary divisions. I mean, I didn't make the point of not seeing disciplinary divisions.

I mostly just dropped the baggage that I had carried during the last 10 years or so.

That's very confusing in a way to me, because you were in this environment that You thought you wanted to be in and then you sort of, got a little disillusioned with it how did you end up in opening back up again? Yeah.

So I would say it was more of a practical change because by the time I was doing my master's, I was determined to do a PhD. I had the academic career in my mind was sort of default by age, I don't know, 14, 15 that I wanted to, I don't know if academic career, but I wanted to get a PhD or the highest possible training in the topics that I was interested about, and that was.

Pure mathematics and theoretical physics. So that was clear. So I just found a PhD and he happened to be in a more math. It was in the mathematical physics group, but it was on the differential geometry side of things. So my PhD is just basically differential geometry. There's a little bit connection to mathematical physics, but there's certainly no connection to the.

kind of theoretical physics tradition that was going on in Cambridge and the one that I mostly looked up to as a kid and so on. So, what happened during that, I mean, my PhD was very exploratory. I would say, I mean, those are, those were the years where I learned music. I never learned music as a kid, so I learned to play keyboard and, it was, those were the years that I was expanding into other territories.

Did you see those disconnected, the math

and the music? Absolutely disconnected in my case. So this was a, just a passion of mine that was for many years coming and eventually had to happen one way or another. And I thought, in a PhD, things seem a bit more relaxed because I was never forcing myself to do the publishing and all that stuff.

So. I had time, so I decided to go on that tangent. But the, what I was trying to say is the main the main change happened when I basically realized, okay, I have navigated academia for however many years at that point, like eight, nine years from the first year of undergrad, masters, PhD, and so on.

And I realized. Okay, enough is enough. I need to go back to my original questions. And my original questions have not, I didn't even know the word physics when I started asking those questions, right? Like I, well, where's, what were

your original questions if you had, so

I say questions in plural because there were really almost uncountably many questions in some sense, meaning I had questions about, the mechanisms of the things I saw around me.

And this connects to the sense of philosophy in the most etymological sense. When the, in school, you are taught about Greek ancient Greek philosophy. You get this picture of, the philosophers is walking around and talking about what they see in this very sophisticated way.

And obviously that looked like a cartoon to me. But. But I was like, yeah, that rings a bell to what I'm feeling, because I'm walking around, I'm seeing things that I just want to understand. And I found my first entry into that as with physics and mathematics, because I felt that the, those were really cutting into some very precise patterns that I connected with very intuitively, which was motion and shape and all these kinds of things in the world.

But there were other, there were many other things that I saw that were not directly addressed by the kind of physics and mathematics that I studied, namely biology process of societies and civilizations, economy all this all these more complex systems like

realm. Okay. So you kind of turned your focus back out to an, like what were you saying before about understanding, trying to understand the world.

And at that point, was it more about how these things link together in some way? And also, did that reflect the mathematics that you were interested in at

that time? Absolutely. So, so that's a great transition because I did formulate it that way, like just put it.

I turned towards understanding as a goal, instead of making a career within academia that takes you somewhere, blah, blah, blah I turn it into that. And so, yeah, I happily happy coincidence, it was really coincidental. It wasn't two separate things, but in a happy coincidence at the time, mine, pure mathematical research had taken me to a question that had to do with higher order mathematics and higher order operations, meaning operations involved more than two elements or more than two inputs.

It was a natural question then to ask, okay, so how prevalent are these higher order interactions in nature? And just to, for the benefit of the audience that are just hearing some abstract words what I mean by this is usually most models in science and certainly in, in social sciences and economics and things like that, Assume pairwise interactions.

They assume, that two people come together and they do a transaction or, in, in ecology, you have a sort of a predator prey sort of dynamic and things like that. So they're usually very pairwise. Descriptions of reality. And by

pairwise, can we think of that as binary too, or is it really, is there?

Right. So

maybe it's worth being precise with terms. So pairwise just refers to the fact that there's a two there's a cardinality to, as we say, mathematically, right? So count two elements in your description. In your in your connection pairwise, and you will say pairwise, three way, four way, and so on, right?

Like to describe some form of engaged interaction of an accountable number of elements. And the

higher order is when you can't break it down to that. And exactly.

You say it's higher order when you cannot go below that. That connection, and I'll try to give an example to to illustrate this that is much more social and think easy to understand.

'cause unfortunately the most illustrative example of this is the Borrowin link, which is this configuration. Yeah. I think it might be too much to try to, but this is it's no use to put into words. You just have to see it for yourself. So a good example of this higher order interaction is a friend of a group of friends that all met.

For the first time together, right? So imagine that you're on a trip and you take a lift somewhere and then you meet two people in a lift or elevator to, in your hotel. So the interaction is the three of you, you're all having conversation, taking turns, whatever, but you're all seeing the three of you.

So imagine what the difference between that and between some childhood friend that you met. In school and you had your personal history together. So the interaction that happens with the three people in the elevator never happened in pairs, because it was just, the coincidence of all of you being in the elevator, and then spending whatever 10 minutes afterwards having a chat and then you go your ways that social bond there.

is fundamentally ternary, because, the three of you were always present, you, people were always influenced, every single individual in the interaction was influenced by two other individuals at all times. However, if you have a childhood friend that you spend a lot of time together, alone, you were mostly influenced just by each other, right?

So, so it's a social dynamic that was very pair wise, and in the case of a childhood friend, and someone, some acquaintance that you made in an elevator is something that is very three way. Because it's clearly influenced by the presence of all the other people there. So you would say that's a higher order interaction in the sense that you cannot make acquaintance with several group of people with a single person, because by definition, that's not the case.

And most importantly, when you do make the acquaintance of a group of people in an elevator, you cannot break it down to a combination of pairwise connections because those literally never happened anyway. Right. And the relationship has been shaped by the presence of the third person at all times, right.

In the example.

So, so all those three entities would be different if you separated them than they are in that group. So. Exactly.

Yeah, exactly. Yeah. Yeah. So, so exactly. So the three individuals are different on their own because they are basically non social entities because they are isolated.

If you take the pairs, then there will be arguably there will be similarities, but because they are the same people, but the fact that there's a person missing.

I think just on a practical level, we all can understand that just if you have different social groups and you're kind of a different person and if the groups are really different and you try bringing those social groups together, it's often very strange because, you're feeling like two, like maybe it's your math friends and your childhood friends or something.

And yeah, so I think we all understand that we're different. In group. So if you start with that, then you can never reduce it

exactly so. So social groups and social gatherings and social dynamics are actually a very natural source of examples for higher order structures. And so the coincidence was at the time when I was opening up again, or sort of reconciling my scientific childhood self.

I. Discovered this realm of ideas and so my mathematics my mathematical research went into these directions.

Higher order and complexity and things like that.

Exactly. Exactly. Yeah. So my approach is still very my approach is always quite lean. I like to work with small things meaning, small mathematical objects that I manipulate and I have control over their, the complexity, but the goal, of this of these investigations now has changed quite dramatically.

Before it was some kind of grand, philosophically unifying sort of themes of which is interesting still, but now it has a much more exploratory sort of break new ground kind of approach where we are trying to unveil patterns that are otherwise hard to understand. So, so this example of social interactions as higher order as a phenomenon that is higher order is actually just one of many.

And there are many instances in, in, in science today that we have this higher order systems. I was in fact, a few weeks ago in Vienna for a conference in network science. And we were shown out of the hundreds of talks that were given there about 80%. Had in their title higher order or hypergraph or, beyond pairwise, blah, blah, blah.

So it was, and they showed a, one of them showed a graph of the papers published with with a higher order or hypergraph or beyond pairwise and so on in the title. And it was from 2015, 2016, almost none. In the last few years, an exponential growth.

Incredible. What is that? Is it, I mean, because I'm trying to, there's a way in which we're trying to look at patterns between different patterns, which is kind of this category theory thing, like in the hypergraph.

Maybe we can, you can even talk a little bit about what a hypergraph is and hypermatrix in a really general way. But in the big picture, it seems like in the past five years, we've all, Sometimes we reduce it to this interdisciplinary thing, but we're all trying not to get overwhelmed because there's so much information.

And at the same time to try to, maybe as a means of not getting overwhelmed, find these patterns that connect all these diverse disciplines or mathematics, right? Even mathematics trying to, but at the same time There's something about what something has changed in terms of that, that we're the linear model or the binary model, or we've started to understand that doesn't hold at all.

I think. Are you also finding this in mathematics, but how what's the language? How do we remodel that? How do we get out of this linear way of thinking? It reminds me of your paper beyond binaries where it becomes very hard not to use binary language. To talk about getting beyond binaries. Did you see that in this conference too?

I mean, is that something you see in the math?

Absolutely. This is I mean, this is the the heat of the moment in, in, in some sense, the zeitgeist that is going on in, in this sub field is very much along these lines. So it's a very fascinating, it's a very fascinating topic. And this is what I got.

Interested on in the first place. And this is, this was my focus of interest when I first started and the fact that the language that you have to use to describe it is very limited. We are, so there are many ways to go at this.

So one, one aspect is we use sequential information most of the time. And arguably this is, there's a very good reason for this because time seems to be one dimensional flowing in one direction. And so anything that has sequential structure. It is going to encode something like a process and therefore it's going to be terribly useful.

Even

if we think of it as a trajectory again, since we've talked about that a bit, there's always going to be some link to the next point or backwards and it seems linear from that agent base. Yeah,

exactly. From a, from an agent base, it seems linear. Therefore anything that has a sequence built into it is going to be very relevant to these kinds of patterns.

However, Okay. Great. If you try to take the structure of a sequence as a static thing, so you're no longer seeing it dynamically as part of a process, but as a static thing then it becomes more of what computer scientists call a data structure, right? So it becomes something that holds information in some kind of slots in some kind of, boxes in some abstract sense.

And as a data structure, a chain or a sequence is something very specific. It has. A very tight order. You can place a first, the last and things in the middle. And they, any given element has a, a successor and a predecessor. And, it's a very tight concrete data structure.

So if you imagine, listeners are imagining a chain of elements, you can imagine like characters in a register, in a computer, or, a literal string of characters in the piece of paper when you're writing. If you think of that. And you abstract what is the, what the structure of that is, it's essentially a chain of points or nodes and pairwise links, first character, one node, next character, link between them, next

character.

So every point would be linked pairwise on both sides, maybe, but always only. Yeah,

exactly. But pairwise, but only also in this one dimensional sense. So one way to depart from this one first initial way to depart from this, which arguably has been relatively well explored until now is to break the linearity and or this sort of chain like nature and become more like a network.

And then you become like trees or you become like, cyclic networks and,

So then we have more nodes, right? So if people are trying to visualize it, instead of this kind of sequential, almost linear, one dimensional thing, we're sort of opening up the dimensions

I'm trying to build you towards that. So you go from a basic chain of nodes to something that now every node could connect to more than one or two. So you basically grow it's still like a web of pairwise links. Right. But you can, connect one node to four or five and those connect to other four or five, but still they are pairwise connections.

Right. So these, this is the subject of what has been called network theory. This has been going on for maybe, I don't know, 30, 30 years now or something. It's a fairly. well established field of research. You have several textbooks that are very good that have, very well condensed knowledge and techniques to analyze these things.

And it has been one of the enablers for all the technology that we have today. I mean, this internet that is sort of enabling this conversation right now is very much based on techniques for network theory to make sure the algorithms are fast enough to, process signals and things like that.

So, so that's one thing. Now. What hasn't been done so much in all this time is to generalize the pairwise nature of the connections. So that means what if I have three nodes that are in interaction together? Like in the example, we had earlier about social groups, and I want to express the connection between those three in an irreducible way, meaning you don't have a triangle of pairwise connections between them.

You just have one link, one kind of interaction, like in a network of people, these three met in an elevator. So that interaction. cannot be described as these two made in an elevator, those two made in an elevator, those two made in an elevator, because the three of them were in the same elevator.

Therefore, there's a single instance of a connection there. So in a picture in your head, if you were imagining sort of a web of links between nodes before like lines essentially between nodes, now what you should imagine is that you're starting to include solid triangles, solid sort of squares or solid tetrahedra and sort of larger shapes in this sense.

And so normally networks of pairwise connections in mathematics are called graphs, it's a historical name. And so when you go to this higher order graphs that have higher order links, then they are called hypergraphs, just simply to extend the word there.

So graphs are a particular kind of hypergraph, just without the higher order ones. And so, but in general today we tend to, at least I am trying to enforce the practice of calling hypergraphs, Or networks that look like hypergraphs with these higher connections. I'm just trying to call them networks.

I think it's I don't have a horse in the game to push for the word hypergraph or to push for the word hypernetwork or to push for the word hypermatrix. These are all words to describe things and I think everyone agrees that a network today is understood to be higher order by default.

If you want to specify, actually, it's only pairwise links, then you tell me it's a pairwise network or whatever. And then I know what you're talking about but yes, so, so one of the, just to round up your point about thinking about this and the language and so on. So the main problem that we have in this field, the reason why it's underdeveloped, the reason why there's so much new ground to to cover is that human minds seem to be very bad at holding intuitions for higher order processes.

We are extremely good, apparently to change sequential processes. And that's why programming and the sort of architecture of computers and the entire software engineering history has been so successful because we have built in this sequential ways and people have started to parallelize and build algorithms that are essentially always following one path of actions.

So

you have the zero one binary thing.

Yeah. Exactly. Well, that's one thing. That's one expression is the binary of having two symbols. But what I'm referring to is more the fact that you can chain actions one after the other. And the state of your system depends only on input output. Sort of, a framework where you're in this state, you get an input, and then you move to the next state, you get an output.

Yeah,

this is kind of, this makes a lot of sense to us. This is how we, this is the frame. Yeah. For even our language and coding.

Absolutely. It's everywhere and it's extremely powerful. I'm not here to try to diminish in some sense that power that no.

It's been a wonderful tool. It's gotten us

very far.

It's an extremely powerful tool and super useful. However, mathematically, it seems clear, both mathematically and empirically, because all this phenomena that are higher order that can be broken down into pairwise connections, it seems fairly obvious that there is a world Of higher order, call it higher order processes or higher order computation or higher order algebra, if you're more mathematically inclined, where the things that you know, the intuitive phenomena such as people gatherings in, in, in groups, or if you're familiar with the Borromean link and not theory the topology of a network of interactions, or, three way symbiosis in an ecosystem, things like that.

These, yeah. There seems to be clear evidence that these things exist, and there is a science to it. There is some patterns that are there. Now, human minds are terribly equipped to deal with those things immediately, mostly because these are arguably sort of either very specific phenomena like social interactions, in which case, brains, human brains are have entire subsystems dedicated to dealing with them, or they are very far removed from intuition.

So things like knot theory is kind of a very specific thing that you don't have intuition about it. You don't know what it looks like, or the sort of interactions that are being found in nuclear physics that have, I mean, these are very counterintuitive things, or, multi way entanglement, higher order entanglement in quantum mechanics as well is another topic that, these are very, under intuitive things that are not in daily life.

So it makes sense that we have not evolved a natural capacity to deal with higher order structures. And yet

we've noticed them. So there's this weird tension, right? We've, we're sort of pushing into a new space, but we can't quite, we're not prepared, we're not easily.

Able to access it yet.

And that's the main, to me, that's the main so, so, okay. So in a way that, that aspect, let me formulate it, let me verbalize it clearly. So the fact that you have a, an area of research that is. Difficult to put into words is difficult to articulate and it's difficult to think about in a way it's precisely what I find the most attractive about it because it's it gives you the opportunity to do mathematical engineering in a way it gives you the opportunity to do or more generally conceptual engineering in a sense that you can develop ideas in a genuinely organic and original way, right?

You're trying to map out and chart. An experiential territory that is. unfamiliar, that is uncommon, that is underexplored. And, when humans develop language for certain phenomena they were engaging exactly in the same situation. In today's world, I think it's hard to find the realms of of novelty that Say physicists in the early 20th century were finding or geneticists or biologists were finding in the mid 20th century and things like that, where there were entire realms of empirical evidence that were uncharted.

First time that you realize that there's a molecule that is essentially a Sequential crystal that has essentially digital information about hereditary traits in animals. It's wow. Yeah. Yeah.

It's an entire universe to map microscope or the telescope where you're studying all other worlds within what you thought was some one world.

I think we're at a moment like that and this is going to be a little messy, but I want to push at this stuff you've been talking about a little bit because I definitely feel like a lot of us are in this frustrating space of knowing there's some other way. And we can almost sense it, but we can't put it into language.

And as you were saying, part of that is because the language itself has been built on this binary way of looking at the world, which isn't a bad thing. I mean, let's look at philosophy again, right? This Descartes, Descartes gets a lot of slack, right? About dualism and that we've, that we look in the world as either it's mental or it's physical, either or, this is a really basic structure of our languages, all of our languages, our mathematics, as you pointed out in your work.

And it's been great. It's helped us get somewhere. So we're not saying it was wrong, but what we're seem to be trying to do is unstick ourselves from thinking of that as like static and a fact and more like, Oh, that's something we've been using to get somewhere else. And this is where it might get messy, but when you were talking about the sequences and the pairwise, so we were talking about an agent base, it's what I call an agent base or a position or a point.

If we just go even to that, isn't it that's also beginning to change? And I think we could open this up. In terms of ecological issues or anywhere, this, or the idea of the self, right? That actually that position itself is not just one position. This goes to the physics too, right?

Yes. That is certainly the moment that we're living in. We I like to say that higher order science requires higher order thought. And so higher order thought. Has to build on the framework that we have so

but you're also creating a new language in a way And it

is it has to be created in a new language.

That's whether

mathematical or I mean Separate right mathematical

exactly. No. No, I mean, I wouldn't say I mean languages Language is language, I would say. I mean, if I say verbal language, then I'm implying something better, better suited to a linguist or something like that. If I'm saying mathematics is a language that's more suited to

Well, yeah, but even to think of Descartes or something, if you and your team or the Wolfram Institute or something comes up with a way of understanding this mathematically in that language, that's going to actually end up changing English, language too.

Possibly yes. I think, yeah, I'm I don't, maybe this is a bit controversial. I don't know, but I might put it out there since I think this podcast is definitely receptive to

controversy

is okay. Controversial opinions. I mean, it's not so controversial, but it's one of my opinions that are perhaps less popular with the philosophers.

So, So this is going to sound very contrarian, but I'll just go around with it and then maybe I clarify afterwards. So if you think about human modern societies in a historical sense, so, going back to Babylon or Egypt or ancient Greece and, or China and all these places in the world, um, Mesoamerica, like all these places that were developed, Developed civilizations that had arguably, as far as we can tell, languages that were grammatically and lexically as sophisticated as ours today as, English today or Spanish, whatever.

So, I always like to think of some kind of Almost a thermodynamic argument about, if you have human beings that are physiologically similar, we are still for a few thousands of years physiologically similar, that have similar verbal language structures. There has, so if you have these societies engaging in relatively similar frameworks some kind of organizational structure that puts specialization, it puts some value into specializations.

You have like academy like environments, you have school like environments, you have training, you have, a discussion sort of forum like environments and things like that. My opinion is that verbal language literal verbal language, and this is to discuss, talk, debate, write, read, this kind of mode of operation is it's only going to get you so far, right? I think it's going to get you to a certain level of development of intellectual development that in my opinion has been, has a tap in a conceptual sense, not in an extension sense, because I guess in terms of extensions, you can grow indefinitely in some sense, but in terms of, I don't know, call it sophistication or cutting power or in some other direction, it has a limit because it has a natural sort of feature limit, right?

It's the structures of verbal language are more adapted for this and that ways of communicating information. And therefore, so, it has its limits. So in my opinion, after thousands of years of these kinds of structures, I would make a thermodynamic argument that you more or less reach. a thermal equilibrium of the kind of ideas that can be developed.

And this is very unpopular because it devalues or seems to sound like it devalues generating new ideas just with verbal language, which is what most philosophers do and writers. And I mean, I myself do it. So, so however, what I like to think is that the moments in history, at least from my point of view, that have seen a clear departure from verbal language.

In a scientific way, have usually led to to very big developments in, in, in science. And so if you think about, so this is basically the history of mathematics. Can you give me an example?

Yes. So, so the history of mathematics in the sense that you, the invention, my favorite example is the invention of calculus in the 17th century Europe.

That's my favorite example, because I think it has been. Probably together with quantum physics and in the early 20th century, but we are still seeing the ripples of that to play out today. I think the ripples of calculus have already fully played out. In a way, and I think it's a more or less a close story that can be told.

So you have, and let me make my, let me see where, show the audience where I'm coming from with the, this historical example of calculus. So you have the science of mechanics, the science of the motion, how things move, stability of buildings, of structures, machines, things like that bows and catapults and building cranes and all that stuff, all that science.

you have from, as, as old as a modern civilization, right? As, tens of thousands of years old. The science since the Babylonian, the Egyptians, Romans, Greek, Chinese, Mesoamericans, the science itself has had not developed a lot. You compare Egyptian mechanics to Chinese mechanics that were, had very little contact with each other, mostly the same.

You compare Roman to Mesoamerican, mostly the same. Right. There's no fundamental great changes among them. And what you observe in history is that the sort of societies that developed were quite similar. I mean, you had empires. tens of thousands of years ago, and you had empires hundreds of years ago, and they were similar.

They had similar infrastructures, they had similar, sort of organizational layers and things like that. However, you move on to 16th, 15th, 16th century Europe, and the conversation that was going on around motion, and you have this clever people that have had a lot of free time to think about the concept of motion and the connection between motion and geometry and they were thinking in these terms of, okay, but if something is moving, it's moving in every infinitesimal moment and so on.

And this has been questions that were brewing for many centuries, but at one point, the concept was crystallized that there was a notion of what we call today a function or some derivatives and things like that. So what was crucial about that a contribution is not the topic. Because everyone had talked about motion, everyone had talked about, shape and stability and forces and things like that.

The crucial distinction was that what was invented was a new language, was a combination of a geometry, logic, and and language and verbal language.

It was almost like a written language or something. Yes. That kind of a development where you suddenly have this, External shared representation.

Correct. Yeah.

And the crucial of it, the crucial part of it is that it was not just verbal. It had it had a logical component, which was the deductive part of, if you make these steps, these formal steps with the symbols, you can deduce things, it had the geometric component of it because, you were representing calculus in the beginning.

It was very geometric. It was all about, shapes and tangents and things like that. And I had obviously the symbolic component that you had, a concrete set of symbols that, that you could use systematically, as you say, representational, external representation, and you can communicate it.

So, but crucially, it was not made of verbal language. It was not a system made of words in English or words in Latin. Obviously you could explain it with those words and you can clarify and you can sort of scaffold around it with verbal language to communicate it. But in itself, the core function of it was devoid of verbal language itself.

Right. So to me, . If you look at history after the 17th century when it was invented, you see all the development of mechanics until the end of the 18th century. A year a century later. And then you see the re the industrial revolution that followed. There is a direct causal connection between the industrial revolution and conventional calculus.

There is no

doubt about it. That's fascinating. That's fascinating. Especially because, of course, the industrial revolution had to do with all these new tools that we build. New, which depended on, on that in a way. And I said it's like written language, but I mean, when we first started writing that changed society too, in a way.

And it's also interesting though, because it sounds like you're saying there wasn't a continuity, but just the fact that it wasn't like Leibniz and Newton or this, the calculus was coming from a lot of different people at the same, so there was also some kind of way in which. What, what had developed, it does feel similar to now, like this tension and this frustration I was describing where I feel like maybe there was something like that then too.

And that was kind of the release of it, the calculus. Absolutely.

Absolutely. No, I like your example. And that's a very good example. The invention of written language. Yeah. I think, uh, it has similarities because you can't go back, exactly. You can't go back. So this is the feeling you can't go

back and we can hardly even imagine what it was like before the calculus or written language.

Exactly. So, so, so to, to run back to the reason why I was making this point is that, I feel, I like to believe that in, in a humble way here I wouldn't get cocky because we don't know, but in a very humble way, I think that what, the way I like to see my work, my mathematical work.

is like being in the conversations in the early 17th century about the concept of calculus, but for the mathematics of higher order interactions and how higher order systems ought to be represented mathematically or can be represented mathematically in an efficient way so that we can make progress in, in the descriptions that we have.

Because obviously the kind of problems that that you know, Newton and Leibniz had in mind were problems that had been and results for millennia, but there were techniques to go at it. I mean, there were other ways of solving these problems and they were relatively successful. So it's the same thing today, right?

Like there, there are many ways of attacking this higher order interactions because effectively the world is higher order by nature in some sense, right? But the techniques that have been used so far are Good, you know that they are effective. But the question is, are they efficient?

Are they, could they be improved in this sense? And I feel like we are glimpsing a situation that probably is parallel to the moment of the invention of calculus because there seems to be a lot of phenomena that Is that are similarly unexplained, and they all have in common this sort of aspect.

So we are hoping that we are going to be riding the wave of this kind of change and very much that we are very consciously aware that the change is in language is a matter of language development. Moment. And in fact Newton gets most of the credit because of history and so on.

But actually, knits had a much more diligent notational tendency. So the knits notation is a notation that we used today, actually. Yeah. And a few years later when the science was much more codified, it was put into modern symbols that, that we recognize today.

Like integrals and derivatives and limits, all those things that notation effectively ushered the revolution in this sense. And, the engineers that, that worked during the industrial revolution, they were all trained in calculus. They were explicitly trained in calculus. So what difference did it make to be an engineer in France or England in the 19th century versus being an engineer for the Roman empire or in the Babylonia?

really at the core is that they all learned calculus for a few years in an academy and then went on to basically try to do the same things but they had much more powerful tools, right?

That's a wonderful connection to make. I really never had thought of it like that and especially not in the context of how it feels right now and that we're on the edge of something but so that's beautiful.

I'm going to be thinking about that but what do you think is going to be Is it algorithms? Is it coding language? Is it, of course, we already said all this is tied together because you can't, you gotta change, it all changes at some level, but what's the. What's the medium, do you think?

That's a great question.

Thanks for the question. I am actually working on what the answer to that would be, which is we are developing a, so it's going to be computational. I mean, long story short, it's going to, it's going to usher all this sort of computational ecosystem that we've built for ourselves. The fact that we have these machines around us that automate many processes.

Steps of things that we know how to do, but they do it, millions of times per second. And, it's much faster. But the, so to answer your question more specifically, one direct way that we're going to try to accomplish this is by creating what we are calling internally, the blackboard of the 21st century.

So the blackboard has existed, as you said, invention of writing and so on. The fact that you draw some things on a surface has existed for as long as we were humans, probably before. But the fact that we, the mathematicians essentially have done all their work, if you think about it, in terms of tool use, mathematicians in the last 300 years, all their work, all they required was their minds.

Their life experience, which, this comes for free for humans walking around the earth today and a piece of paper or surface that blackboard to write on. Right. Yeah. So what we're trying to develop is the next technological step from that. So it has to, in some sense, reduce to that in some regime, it has to be sort of a generalization of a blackboard.

I'm going to say blackboard instead of piece of paper, just for the

romantic. Well, that's the trajectory. So it's going to be continuous somehow.

So it's going to, yeah, it's going to, it's going to extend the functionality of a blackboard. So you could, in principle, just use it as a blackboard. But the way we want to do it is that the blackboard itself.

It's computational in a way that you have direct control over. So you have many programming languages nowadays, and they are all computation. You can code and you can set up your own code and experiment with your code and explore ideas with your code. This is something that absolutely is possible.

Very accessible languages like Python and it's very accessible. Mathematica itself is a good exploratory language and strong. But what we don't have is something that is as intuitive and as direct cognitively. As writing strokes on a surface and that becoming something cognitively functional, right?

So most mathematicians nowadays would sit, mostly think about something, sit down, draw some diagrams, write some symbols, then come back, manipulate those symbols in their heads, write something else and so on, right? And so they would effectively do this process of rewriting symbols. on a blackboard or a piece of paper, and then do a lot of thinking and imagination in their heads and so on, right?

So what we want is that the interface doesn't change much, so what you actually engage with is some kind of surface or screen or digital space that is showing you some symbols, pictures, diagrams, the shape of things are not going to change much. The direct engagement with the substance, so to speak, is the same, but what's in the background is a system that you also set up.

via drawing diagrams and writing symbols and so on that actually computes things automatically. So to to give you an example, it was like a

smart blackboard, but in a really dimensional

way. Yes. It's a very multidimensional smart blackboard. The most important thing is that it doesn't do anything that you don't, that you don't tell it to do.

So it doesn't have, it has the computational capability, but it's not a computational blackboard. So let me put it in an example. So if you write black one plus one on a blackboard, right? Just the symbol one, the symbol plus, the symbol one. You, the blackboard doesn't know what those symbols mean. But if you have arithmetic loaded in your head, because you have a set of rules in your head that tells you, okay, there's this alphabet of symbols, one, two, three, four, five, et cetera, just whatever.

And there's this special symbol of plus, And there's this maybe a special symbol of equals or outcome or whatever. Then if you write one plus one, you can run the algorithm in your head that tells you, well, one plus one points to two, and therefore the outcome is going to do to be two. So you would write equals or your arrow or whatever two in the blackboard.

So the idea is that you could teach the blackboard to say, well, x plus y equals at the map or something, like you, you could set up the rule that you have an alphabet and you have a way to navigate the alphabet by a single rule. So you could teach the blackboard that by simply writing it.

And that's where the computational part of it programming

is just writing it. You're training the algorithm just by using the tool.

Yeah, exactly. I mean, in some sense you are coding the blackboard just by using the blackboard in a diagrammatic way. Obviously you can't just scribble a random thing.

You have to kind of more or less limited in the version that we have, you have to follow some kind of constraints of grammar. But it's not like a programming language is really drawing a diagram. You draw the diagram, the system interprets the diagram. And the diagram codes a way effectively in the machine level codes a way that is going to perform an algorithm.

And then from that point on, you can apply that sort of computational knowledge to our computational framework to whatever comes next on the blackboard. So effectively your blackboard becomes this sort of outsourced comp thinking machine that will perform steps. That will take you, minutes, hours, days, years, decades.

in a matter of seconds, right? And it's gonna allow you to draw sort of symbolic steps that are much much longer than you would normally do. Okay.

That seems really cool, but also really could, if you're, If you're wrong and you write 1 plus 1 equals 3 or something, then it's gonna, it's gonna learn that.

So is it, what's the, is it connected to every other blackboard or something? No,

so there's no learning, so there's no learning. So there's no, in principle, the tool we're building hasn't, doesn't have any learning. So you don't So

it's not a generalization kind of

thing. No. So we don't use any, I mean, learning will just be a weak analogy on how to explain how it works in the sense that nowadays learning this all kinds of machine learning systems.

There's nothing of that in the one that we're building. So it is really coding with diagrams. I mean, the best way to

explain this is like a faint Feynman diagram kind of. But yeah, that's that

could be one electronic like exactly so so you could you could I mean, this is actually directly inspired by category theory the way category theories work.

They mostly draw diagrams, they draw arrows and, between letters. That's mostly what they do, right? So they draw these diagrams with arrows. They think hard about them. Then they draw some more diagrams with arrows. They think hard about them. They draw some more diagrams with arrows and that's literally their workflow, right?

You observe a category theorist over a course of a month and you, what you would see is they walk around, they do human things. And when they do their math, these things, they basically sit down, produce diagrams with arrows. Think hard about them. Produce more. Produce more, and then eventually maybe write a paper.

That's it. That's the workflow

The distinction here is that what this blackboard of 21st century does that a blackboard from the 20th century, it doesn't, is that.

you can code the way that you're going to manipulate your diagrams, which is what normally we do in our heads, right? So you can actually code that in a computationally active, it's sort of alive. It has life of its own. You can infuse life into your symbols in the blackboard, which is something that we do virtually in our heads.

Mathematicians do that in their heads anyway. So what we're trying to do is to outsource that information. To the computer to the sort of black box that is in the background that you don't see directly and you interface with as a diagram like as a piece of paper that you draw symbols on and then the idea is that those symbols that you draw inform how the symbol the other symbols that you draw.

Later on can be transformed so that you can do steps that would take, years to compute by hand. You can do them in seconds. So eventually you can develop a sort of a feedback loop with the interface that instead of just literally write something. I observe it. I keep it in mind. Think about it.

Imagine how to manipulate it, then write something else. Yeah. In that step, right now, the paper does nothing. Let's put it this way. A paper, piece of paper or blackboard, is a computational machine that only holds memory. It doesn't do any other computation than just holding memory. Meaning, you write something, it stays there.

Right? So it is, in some sense, it's a computer. It's just holding memory. It doesn't have any CPU.

This reminds me of what Jonathan Yeah. This Gerard, I think, is that how I say it? Gerard, yeah. Yeah, it was, this program. That he was kind of using that. I don't know. It seemed to be sort of just storing the memory of all his past equations.

And then he was just kind of keying in very minimal information and getting.

That's precisely the kind of mathematics that Jonathan is part of the. Part of the institute and part of the project. And that's precisely the kind of mathematics that we are using in the background.

So we're using these things called rewrite systems and this framework of you can modify the state of your computational

entity. That was powerful. There was something very exciting about that, but this is an expansion of it so that it's more interactive

Well, it's, we're basically just building an interface for it.

So we, I am adamant in having a, an interface that Can mirror what we do exactly with a blackboard and I don't mean it in a smart blackboard way in which you basically have a screen that you write on with your fingers. That's what I'm confused about. Yeah. Yeah. Yeah. No. What really means is you interface with the system.

Like you do with a piece of paper of a blackboard, like that's literally your mode of interaction. It's not like it's a screen on the wall that it looks like a blackboard and you look, you call it a smart blackboard, which is what smart blackboards are. They're really just screens that you touch on with your fingers, like with a pointer.

This is not it. What it means is that you have a way to draw diagrams to write effectively code that is. Very human centric that you can just organically draw with your fingers that the system can interpret in a computational way. So you could, another way to put this, maybe more, more, more clarifying, forget about the term blackboard and think about it's a diagrammatic programming language.

You're programming with diagrams. So you're programming with like squibbles. It's like you, you do a squibble of some kind of symbols that can be an organic programming language.

So it's almost like object oriented programming, except more connected to the actual, I mean, almost like you could.

You could write. Yes.

Yeah. So instead of actually so it doesn't matter what kind of programming you do in the background, there are many possibilities. You can, go wild with the sort of programming that you go you do in the background. But what's important to us is that the interface for a mathematician Would feel directly relevant.

So if you're writing diagrams in a piece of paper, a arrow B or, one plus one, things like that, the system will, if you decide to, mark them with a distinctive color or something, or, box them and say this or whatever, the system will actually keep that as a computationally active, computationally meaningful, a bit of information so that you can use it later.

And because right now when you learn arithmetic you know about the algorithm to add to numbers. If you're given to base 10 numbers you have an algorithm to do it, right? If you actually had to add up, several figures of numbers, most people that are great at that sort of computation, you would just write it down and go through the process, and actually write down symbols.

So that pa paper keeps memory and you are the computer effectively, processing through the memory. So the idea here is to basically export. That to a computer, which is what all computers do. This is nothing new, but what is hopefully new and what we're trying to contribute is that the interface, which is writing on a piece of paper symbols that remains the same.

So you are literally inputting your code into a computer. By writing diagrams like you do on

a piece of paper. So it's almost like mathematical haptics or something.

Yeah, that's one way to put it, yeah, mathematical haptics. Yeah, I think,

I'm not quite getting it totally or how it's different from the way that the computer already computes. But I think that's part of that's showing that it is, you're doing something new, right? Because I can't quite understand, but Yeah, I guess to try to bring it back to the calculus thing. So what did calculus change? It gave people this shared way of doing computations that allowed them to build completely different kinds of tools and ultimately a kind of different world.

So how do you, how would this be comparable to that kind of? Yes.

So, well, calculus, what calculus gave us was, as you said, it was a new language. It was it was entire symbolic system that has an internal logic that represented parts of the world that were not well articulated otherwise.

And the example I'd like to give very briefly is if you try to describe the shape of a trajectory with language, you will have a very bad time. It's helpless, right? If, I mean, I mean, if it's a straight line, you say it's a straight line, okay, it's enough. But the moment it has some curvature, all you can say is it's not a straight line.

That's basically as far as you get with language. However, with calculus, that's the game of calculus. That's exactly what calculus does. You write down a formula and if it's the parametrization of that shape, you're going to see that shape when you execute that formula, right?

So

this can give us a way to, to visualize, to see other dimensions or some, something in the way that we were talking about with the nodes and the hypergraph. So

What it gives you is in a way you're not going to. see anything new, but you're going to have a language that is articulated for something that we already, it's like calculus didn't discover anything in the beginning, right?

Like it didn't break new ground in terms of experience for the mathematicians or the scientists, right? Like they were just looking at cannonballs fly through the air or like objects falling and, inclined planes and things like that. They didn't discover anything new immediately, but they obtained a language that articulated, formally articulated, logically articulated, with symbolic algebra and internal logic sort of operations, what we would call today computation, computationally articulated a realm of experiences that was basically forbidden for language to go into, because language couldn't articulate shape and motion well.

And this is famous for all the. Paradoxes of, in the past and the Greeks and Sino paradox, all those kinds of things, all those limitations were because we didn't quite have the formal language, the formal system, the computational system that allowed us to articulate those parts of experience and calculus, in my opinion, what I call calculus is the invention of that language that articulate.

And how did that translate eventually? Does that, did that help us then understand how to Build movement in a way I'm trying to think of the industrial revolution, make this connection of what was the calculus giving that suddenly allowed this completely different interaction with machines.

Well,

I would say it gave all the modern machines in a way. Yeah,

but was it through this giving, cause you just described something really important about being able to put language on things that were off limits or forbidden before. And that I can feel that that's a rush then of yeah, so so so

what is that because it's not just So the things that were in the world, right?

Like motion was in the world, but the, what calculus did is it gives, so a language is not just the words, a language is also the grammar. So it has computational power, right? You can, it has an internal logic that you can articulate. So because you could articulate, if I build. a wheel of this size and this weight and I attach this string here and I attach this spring there and I model these by some virtual things by some theoretical model of a machine.

I'm going to run some calculations and that machine is going to fail. If you imagine the power of doing that on a piece of paper. Instead of actually building the machine and having it fail and refine it, which by the way, was the way that machines were built basically until that point, then you can see why this was a big difference because things were computed and they were optimized theoretically on a piece of paper and a blackboard.

Right. And then you went to the workshop and you said, look, You need to go for this diameter, this weight this parameter, this and that. And then you build a machine that of course still was refined, still failed and so on. But it was already in a space of design that was so much more streamlined because the mathematics that were modeling it.

were much more proper to the phenomenon itself because calculus was used in the process, right? The mathematics that were used before this was just basic geometry and they're just basic proportions of the length of this the weight of that, that those things existed before calculus.

What didn't exist is that you could put those things into parameters, into equations, solve integrals, some derivatives, blah, blah, blah, do some symbolic operations. compute some numbers and then get answers that didn't exist before calculus, right? And that's what really

changed. So I'm seeing now if let's just say that the hyper blackboard or whatever it's called builds a new language.

So the new language would be illuminating these links and give us, it would give us some way of beginning to understand how to link like these patterns to patterns or these irreducible higher order interactions in nature. So ultimately that would actually change again, right? How we understand the self, we might begin to think of selves as multiple, or maybe we'd be able to visualize what.

what life and ecology is in a different way. And also like quantum computing, it would change something like that too, right? Like how we could visualize.

Yeah, I would, I don't know if I would dare to say that it would change something, but it would certainly expand. Give

language to it.

Maybe. Yeah.

Give language. That's right. You put it perfectly give language to articulate it. And eventually the hope is that if you look at the pattern of the industrial revolution, it was, so you do this theoretical work, you effectively invent a new language, new symbolic system of calculus, derivative functions, all these things.

And with time you have all this output in practical life. And I mean, basically changes human existence forever. Right. So that's, I mean, in a very humble way, we are in the sort of, theoretical stage in which we are sort of like dealing with things that we don't understand well, like the cannonballs in the 17th century.

And we're like, okay, how can we model this? And we are sort of beginning to develop the language with this sort of hyper blackboard, as you put it and sort of giving the tools for mathematicians to possibly engage with it in ways that are intuitive to them. And so it really is kind of a, we're trying to put ourselves in, into this position of we're, hopefully ushering a future era of intellectual development and technological development eventually, but it's much more within the digital realm of computing within the abstract realm of mathematics and understanding, But eventually will help us to understand the systems that you mentioned, like higher order relations in life, how humans relate as well.

And we hope that it will have an impact because obviously having calculus as a tool has had an impact on everyone's concepts. A lot of people think about grabs and rates of change and things like that. For people who

have never think about calculus or use it directly, it's changed the systems and the frameworks and the parameters and the constraints.

We've been talking a long time, so I want to bring it back to this dichotomies, but, and also the personal realm. But so for me personally, this is exciting because I feel like it's so hard to visualize all these different paths, these different nodes, these different graphs the way that everything can be graphed from in multi dimensions from different angles, different ways.

And at the same time, I feel like getting a grasp on that is going to be how we get a grasp on a lot of the bigger problems that face, The planet in a way. I mean, just in general we do have some urgent issues and it doesn't seem disconnected and it could also go the way like the industrial revolution that wasn't altogether positive.

It was positive. And then, anyway, so for me, that's all very exciting. And just to bring it back to you we went kind of off in the mathematical realm, but let's bring it back to your realm, like with the society where you're Linking disciplines and things like this. Do you feel like that's gonna, that too is trying to find a different language because it's not, I know you don't like even interdisciplinary and transdisciplinary, you don't really, you think of that more as a consequence, right, of something else that's happening.

So I don't know, how do you see those connections?

Yes. Yeah, very much. I think you're correct as well. I think of interdisciplinarity or transdisciplinarity and all these kinds of, where it's a disciplinarity. And so I think of them as consequences of an approach to, to knowledge that is more going back to some way of going back to basics where the value of a specialization, the value of expertise, the value of going or building high.

Okay. on, on traditions and, sophisticated ideas and composite ideas. But at the same time, you never lose sight of where you come from in the sense that the goal of science, the goal of inquiry is very, it's very, um, primitive in a sense. So, To put it very bluntly, nature doesn't care about your human traditions in some sense, right?

Nature doesn't care if you organize yourselves into chemistry, into chemists, physicists, and social scientists and whatever. Just, the world is the way it is and we are making sense of it in certain ways.

And we are that nature too, in a way, exploring possibilities. We are, yes. But it doesn't care for one particular possibility, I guess.

Exactly.

So, I would say it's very much that. In terms of building new languages between them, in my humble opinion, I think mathematics is the consequence of that striving for finding a language across disciplines. I think mathematics by almost by definition, I would say is the interdisciplinary language.

I think to call mathematics a discipline into itself is a little bit disingenuous in, in, in that. Certainly, there's pure mathematics that becomes a tradition, sort of an intellectual culture, and it has its own reference, and sure, that becomes its own thing, and you can call that a discipline, no problem, but mathematics as a phenomenon in humans, right, in civilization, I think, I wouldn't think of it as a discipline.

I think of it as precisely the manifestation of of the development of an interdisciplinary language because if you think about it, it is. I mean, it's the

blackboard

Exactly. We humans interact by mathematics, right? Everyone. All transactions the history of civilization can be reduced in a very simple, simplistic way, but you can do this to the history of sort of quantitative systems being implemented to formalize transactions there were previously intuitive or sort of, person to person based, right?

So you have the development of money, of coin of, the development of institutions, of law, all these kinds of things. What I'm saying is that the claim here is that mathematics Is the fact of an interdisciplinary language and the supporting evidence I was trying to point out is that, whenever you have interaction between communities, not just disciplines of a university department in Europe or the US, but literal communities that are separated by a notion that haven't interacted for thousands of years.

The ways in which they engage with each other than killing each other, whereby building things like commercial agreements and, laws and regulations and things like that. And although people don't normally assign, they don't normally recognize law. As mathematics, I mean, I would say that in some loose sense that I would consider that mathematics because, it's a system of rules that tries to be self consistent, of course, it has a human component that is doesn't feel like mathematics at all, and it probably shouldn't, but I would claim that.

Law is a manifestation of sort of implemented logic in human systems, right? And and I mean, if you go to commerce, perhaps it's much more clear because you have a monetary system, you have sort of a ways in which you quantify the all kinds of transactions. And that, that has been the interface of civilizations since we've had civilizations, right?

And so to me, that's a very clear narrative that is kind of complete. You go from the very fact that you can go around the scientific university, or technical university and, knock on people's doors regardless of their department. And if you say, oh, you understand what this graph means, this function here, this probability distribution, this basic algebra, they all understand, right?

Like they all know these basic stuff. If you go and say to a statistician, you know what this protein in this virus is doing, obviously, I don't know. Right. So, so that is the claim I'm making here. I think mathematics is very naturally this interdisciplinary language already historically has been, I would even claim that's what mathematics is, in some sense is like the result of the need for communication between different communities and different individuals even eventually.

So, Looking into the future, I would say that, yes, mathematics is going to continue to be that. Now, of course, we have a framework in which mathematics and computation is getting blurred, and very conveniently so, because we, it's the mathematics of the time. It's, the process is going to be the same.

We're going to be building languages, symbolic systems that we can refer externally, intersubjectively, and, they codify some kind of reality that we all experience and we can communicate and so on and so forth. So I think that's very much the pattern.

Well, okay. I mean, I'll push you just a little bit.

I think I understand math as a sort of universal language, but of course a lot of people don't speak that language. I mean, in STEM, yeah, but when you think of something like art and humanities and then it sure, but we all do use math in a universal way, I guess.

But to get back to this pairwise binary multiplicity thing, and also what you were saying earlier about your. You founded the society and you're interested in this larger group category kind of, kind of thing. What about the math like there, I mean, in everyday life and in the reality of your everyday life when you're just you and how does that play out for you?

Are you cause you, it seems like your math journey and your personal journey. Or even your science journey and your personal journey have always been in dialogue and you're kind of in a new place now it sounds does that, is that reflected in your personal life and like your relationships every day and in reality too?

That's an interesting question. I would say in general, you cannot trace that much of my mathematical trajectory with my personal social trajectory. I mean, as much as you, you can correlate My love for mathematics, my love for music with being whatever, less socially inclined, as I said earlier, or, less interested in maybe just socializing and going out for parties and things like that, other than, exploring things on my own or.

Apart from the correlates in that sense, the manifestation of mathematical ideas or philosophical ideas and sometimes, because I should say that this higher order approach is really, when I said mathematics, I meant it in a very loose sense, right? I mean, it's mathematics in a very broad sense. If you have a system that is trying to be self consistent and sort of self correcting and have some degree of internal consistency, I tend to call that mathematics.

But of course, people don't call that mathematics many times because, a code of law is that. and most people don't call those things mathematics. But anyway. So, so in this very general sense of mathematics which is again almost like you could almost think of it as like A rationalist analytical philosophy in general, right?

In a non scholastic way, right? In a non scholarly way, rationalist and analytic. But I would say in a more direct sense of rationalist and analytic, that's what I would call mathematics very broadly. So it actually brings this philosophy. So the question of higher order interactions and going beyond pairwise and so on, has Definitely shaped how I see the world when I started to get into it sort of more intellectually.

I have to say that before that the things I mean, when I looked at the world, I saw the natural higher order sort of component of it as being there, right? Like it's I saw that, a shape is a whole shape. You can't even if I cut into pieces, the pieces separately. are in a higher order relations when they come together and form a higher shape, right?

A full shape. So in some sense I've never really had this idea of okay, I'm thinking pairwise binary, and then I now go to higher order. It was more like, I just see, the mess that the world is all this complexity around me and all the patterns and so on. And I've been trained into this pairwise models.

I have been, I have learned the patterns, both societal and intellectual to observe those aspects more prominently. And that was, and that has resulted into a very powerful a very powerful process of analysis and, and the proof is we are here and it's all very successful. But it has also meant that the situations where higher order interactions are relevant have less prominence and have less, You have less experience with and therefore you when you have to deal with them, it becomes much, much more problematic.

So one aspect of this is in romantic relationships. And I think this is something that a lot of people have alluded to in the context of the philosophy of love between humans and so on. I think there's, um, there's certainly a parallel, I don't think there's direct causation. I mean, I want to bring down the level of of the sort of the mystic that could be read into the connection here, because I really do think there's no causation between me having explored sort of polyamorous relationships at some point in my life with me doing research in higher order mathematics.

I really don't think there's any. You don't think

there's any connection there.

No, I'm saying no causation,

I'm saying causation, correlation, but not causation.

Yeah, there's certainly correlation. That's a fact.

So you're saying you don't think because you were studying all that you decided to go,

The only causation that could have been the other way.

Yeah. The only causation that could have happened the other way because I was You were

already doing that and so you were trying to understand it. That's probably more likely. That's usually the way it goes.

So I was first drawn into this practice of polyamorous relationships, or, open relationships, whatever.

And I can see that the causality being very specific to the history of the people involved, like myself with my partner at the time, we were exploring and we're like, okay, let's do this. And it was great. And we did it for many years. It was fantastic. It was worked really well. So years later, I get into this topic.

Because of my intellectual journey, and I am a person that doesn't really mix, at least consciously, I am not mixing, my romantic and sexual life with my intellectual life. These are very separate mentally, right? Not because I decide to, but just, they happen almost in like different universes in my life.

They are very parallel. So I don't think, so what I'm trying to remark is that I don't think, I want to bring down the mystique of the causation in my life or the connection between these two things that are directly tied to each other. But what I think is very relevant, which is a parallel between the two, and which is quite a good illustration of what it feels like to do higher order research.

And it's a bit of maybe a spicy connection or spicy analogy is that when you try to go after The, this higher order structures when you try to understand the algebras of like ternary algebras how to be argument are diverse work and things like that. The kind of complexities that you find yourself into are similar to the intuitively complicated situations that you can find yourself into when you involve

yourself into in higher order romantic relationships, right? Because obviously when they work well, they're fantastic. I mean, it's great. As it's more like a love crowd than a love partnership. And it's fantastic, but obviously there's more variables and there's more complexity potentially, right?

There's more complications. And so it's interesting that if you imagine intuitively, the kind of ramifications of complications that could emerge from this higher order romantic relationships. It is actually a parallel to what happens when you study this higher order, higher algebras, because when you study higher order algebras, you literally have this situation that the combinatorics of the possibilities just increase.

Therefore the thing becomes not infinitely more complicated to understand, but a bit more complicated to understand. And it's a matter of taste, how much of that complexity do you tolerate? And this is, the conversation that everyone has, about open relationships and things like that is like, how much complexity can you tolerate to, to exist in them?

Right. So I would say that without getting into that part of the conversation and going back to the mathematics your liking for this mathematical field and this kind of mathematical questions is going to be that, that sort of that, that the answer to the question, how much do you tolerate the added complexity of this?

It's not an infinitely higher complexity. It's not like orders of magnitude is like a different stage of complexity. No, it's just a bit higher, but it is noticeably higher. Like you are in a context where you no longer have the clear. Clear cut equations that are just short. And, like bites of information that you can take in and manipulate, these are no more Baroque, a little bit longer, a little bit more complicated.

So it does involve this higher complications and the relationships are the same, right? Like you, You get this very interesting more multifaceted interactions and, that you can do things that you can never do with just two people and things like that, and that can happen. And it has its own sort of allure and its own sort of dynamic.

But of course it involves all these other complexities and all these ramifications and the combinatorics is just larger, right? So, so it's,

I think it's Does that make it more chaotic or, is there more potential for, I'm trying to think in terms of the math is there any mathematical way of understanding something like jealousy, for example, or

Definitely yeah, no, I mean, it's a simple, I think it's a simple, that's why I think it's such a good analogy or a valid analogy at least in this context is that when the moment, the comparison between binary and ternary, so binary, you're combining two elements, ternary you're combining three elements.

When you. The concept of combining, right, requires at least two, right? Otherwise, if you have a single element, just have it. You don't do anything with it, right? So when you combine two elements, that's the minimalistic expression of combination. That's the minimalistic expression of like composite of some kind, right?

When you go to three the combinatorics of it just plainly tells you that if you have three elements, you can have combination of three, then combination of all the pairs. Yeah. Right. In the set, right? In the group of three. So jealousy is basically, you could say, if these elements are people and they are in romantic relationships, you could say jealousy is just the expression that you have a set of three and the subsets happen to be pairs and a single pairs and a single pairs and a single, right?

You have three partitions of the three elements set of that way. And so you could say that. The phenomenon of jealousy is, I mean, this is a cartoon, obviously, I'm not trying to make any point, but it's just a cartoon, but the phenomenon of jealousy is basically tied to this combinatorics of the elements.

And so, the structure of a pairwise connection this is also something I should say to, to not err on the side of sounding too much like preaching about higher order romantic relation, relationship, which is a higher order network is in general. much more unstable than a pairwise, exclusively pairwise network.

If

you're just Unstable, that's the word I was looking for. It becomes more unstable, like complexity, et cetera.

Yes. The reason being that if you're between nodes are higher order, or, your operations or your combinations have involved several elements and for them to exist, all those elements need to be present.

And that's why we're calling them higher order strictly. Then when one of the elements is missing, the entire interaction disappears. So if you think about the robustness of a network in the sense of how much of the connectivity remains when you remove a node, say a person in a group goes on a trip or just who's on with life or finds a job, or, worst case dies or something, that, that removal of a node in the network makes the question, how resilient is the connectivity structure to that?

If you have a set of pairwise connections in that network on average. Losing a node is going to be the least damaging, right? Just that's, that should be intuitively clear because higher order links require more edges, sorry, more nodes simultaneously. So when one of them is missing, the entire connectivity between them disappears.

If instead you had several pairwise connections between them, if you remove one node, you only miss the connections that connected to that one, not all the others. Be among themselves, right? So,

so that requires a lot more adjustment. I mean, just to think of it in terms of if you're in a relationship where it's three and you're used to that dynamic and one goes and the two are kind of left with, I mean, they have to develop a new relationship.

And then if the third comes back, the three have to develop a new relationship. So, yeah, it's, It can get very complex, but I guess like the jealousy thing or in real life when you're really trying to do something like this, um, like the philosophy part of it matters too, to come back to that, right?

Because in the math, I feel like it's too easy for us to forget about that influence of how you're. Thinking about the situation, like your partner and you obviously had decided, okay, we're going to have a polyamorous relationship and it was like an open disgust thing. So mentally you were going into what was a physical, also physical relationship, right?

But, It can be that there's a relationship where that space isn't clarified, right? And then the complexity can get even more intense. Yeah,

I wouldn't recommend going there to anyone. It's not a yeah I, to be honest, I never, we never made the conscious choice. Verbalized choice to be polyamorous or to open by designation.

No. What I mean is we never made the, we never use a term or found a way to form, to, to formulate it in a very verbally condensed way until years later where we had already done it for years. And then we verbalize it more clearly. What I mean is, everything was thoroughly discussed at all stages.

We were completely transparent with each other. There was no kind of left out information, implied information. It was absolutely constant self regulation in that sense. It was very transparent. In fact, much more than a lot of people would probably

employ. Well, that takes a lot of observation and

Yeah.

And self growth and self knowledge. Yeah. We're young. We're like in our early twenties. And so

Yeah, that's very Yeah. I mean, that just to talk about systems and how they evolve, that's a very interesting model, because it's not the easiest one to take.

No, definitely not. But to us, it felt like it was the most important.

most valuable one. And I mean, again, this is not directly related to any of the mathematical ideas, but we did see some structural resilience in, in high order connections because it meant that if, I mean, here's the thing, right? When you, maybe this is getting too much in the weeds of the connection, but You can have, so polyamory can be low order , right?

, I mean, polyamory doesn't equal high order. This is something important here. I mean, and the network picture will clarify the meaning immediately. So you can be polyamorous and you can be in a network. Relationship, right? Or let's say a relationship network, right? And I'm going to say a pairwise relationship network.

Absolutely, right? You have romantic connections with individuals. And, if you center yourself in the middle, as we normally do intuitively, because we are in ourselves, you would have a sort of a span of pairwise connections going out to other people, right? Like normally, if you are in a more traditional partnership, then you have one single connection going out, romantically or sexually or whatever, and you have one.

But if you're in a polyamorous setting, the default is that you're going to have more than one, right? And so that, Doesn't say anything about whether the connections are pairwise or not. Typically, I would say, and if I might add personally, sadly, but that's just my personal taste, that's not a judgment.

Typically people would have pairwise connections and this is by far the most common and the one that I've also experienced the most which you just happen to know a new person and you develop a pairwise connection. Pairwise connection with that person, but you don't break the connection that you had with the previous romantic partner, right?

So you effectively keep more than one romantic connection going on, but each of them is pairwise, right? You have a two way two way interaction with the people. Now, what you could have is also higher order romantic relationships. And by higher order, I really, I mean, there's like triangles, there's groups of four that are in, in engaged, sort of engaged in romantic, which does

exist too.

And not only in a sexual way, I mean, there are actual people who live together as three or four. And

I have experienced myself for a couple of years when I lived in Edinburgh with my partner at the time, sort of main partner at the time we did have sort of, another person that, that got in the group, another girl that, that was part of a romantic nucleus for a while.

So she was there as much for me as she was for my partner at the time. I mean, I knew her earlier. We were friends before, but when that happened for the time it lasted, It was a very much a sort of a symmetrical thing that was quite triangular and it was quite higher order in the sense. So, so that's why I want to clarify, yeah, no that's a good point.

Not to be pedantic but those things are because the network dynamics, in my opinion, the pairwise network. It's much less sustainable in, in, in practice

because at least, I think we have to talk about space, temporal things here too, because that matters a lot, right? If we're going to look at like over a lifetime very few of us are pairwise.

If we're just going to look at like in the moment, in the present moment, then a lot of people feel like they have to be, even if they aren't actually, because as now that you clarified that a lot of us actually have a lot more relationships going on at once, even if they're not sexual, but than the person we're with it becomes very you have to think about the spatio temporal parameters and also what you're calling a relationship.

Is it sexual or is it just like someone that you're growing with through life?

Yeah. This is, of course, this is just, as I said, it's the spicy analogy. It's not, it's just to spice things up because it really has. It has no fundamental difference to friendship, for example, it has no fundamental difference to acquaintance, it has no fundamental difference to collaboration or co authoring of papers, it really has no fundamental difference to other human sort of endeavors that require some kind of coming together and doing something together.

It's just that it's very spicy because obviously it entices people, all right, this is very close to my heart because we are, sexual

beings. But there is a difference in reality between the way these systems operate, I think. There are different systems and to have a romantic system, complex, romantic system is different than to have a colleague, complex work relationship.

Certainly.

What I was trying to say is that as higher order networks, as far as I can tell there's no real difference. Like obviously our systems are very different. There's nothing really comparing, going. planning life together and going into sexual practices than sitting down writing emails and writing a paper.

Obviously, it's very different activities, but but what I want, what I wanted to say is that for if someone in the audience is thinking, oh yeah, this is wild or just like riffing on something that's spicy for the sake of spicy. Yeah. The actual intellectual ideas behind it, they're not specific to that context, but.

They are a good analogy. I mean, they are not a bad analog of this higher order this higher order ideas and they are quite intuitive. I think if people are normally, my experience is that people are quite overwhelmed. There's usually three reactions to being in open relationships or polyamorous relationships and things like that.

One is. Just being disgusted and baffled. I think that's the minority. Luckily, nowadays, in most countries that I've moved around, the other one is just fear and confusion of Oh, wow, I can't imagine how that would work. It's so complex. It's like I can't imagine. It's like being overwhelmed. And then a very small minority is like enthusiastic.

Oh, right. I would, I'd love to do that because that's how I already do that or something like that. Right. That's kind of the reactions I get. And so the reaction that is the reaction. So take that split of like maybe 20 percent discussed, I don't know, 85%. No, sorry. That doesn't add up to a hundred 75% 75% confusion and fear.

And then there's a 5 percent of. Enthusiastic. Oh, that sounds really natural to me, or I'm already doing it already or something like that. So take that proportion of reactions. And when you look at higher order, the mathematics, higher order algebra, that's pretty much the reaction you get in the community about the one there's 20, 20 percent or so, like a minority that would react negatively towards it.

It's ah, that's a waste of time. There's nothing of value there. Maybe not so harsh, but like some of it is quite harsh. And some of it is mostly uninterested. There's a big proportion of mathematicians and scientists that are like, I am just completely confused about it. I think it sounds kind of intriguing, but I don't know.

I have no idea. I have no good intuition about it. I have no good tools. I don't know how to operate. I think there's a small minority that get very enthusiastic in which I include myself, of course Oh yeah, this is amazing. We have to go after this. This is the future. And so it's actually, this is why I think the spice analogy is kind of fun to make, because there's some formal analogs, as I said, with the relationship network and things like that, and how you interact with your partners and things like that.

There's certainly some formal analogy, but there's also sociological analogy of the reaction that society has towards higher order romantic relationships or distributed romantic relationships and the way the scientific community and the mathematical community per se reacts to this higher order relationship.

I think there's a definite connection and also this binary dichotomous way of seeing the world and how it's been very beneficial, obviously. I mean, we could even think about that in terms of like sexually and in romantic ways. And there's some part of me that thinks And this is like getting kind of way out there, but there is some part of me that thinks, okay, we really do need to get better at understanding that we're multiple selves and that we connect with people in multiple ways and like opening the space for us to, as in our romantic relationships, our friendships to explore that.

Right. And to That kind of does relate to a lot of the themes we've been thinking about in terms of there's some kind of change happening and there's a frustration and there's I don't think those things are all disconnected. Of course, it can get very tricky when you start thinking about like sex, right?

Because that's so loaded. And, there's all kinds of things, but just even a romantic music. Connection and how we see that there's some part of me that wants to evolve right to be able to Hold the space like I guess you were able to do to where you love someone or you have a partner in your life And you're completely okay with them exploring relationships That are not in your pairwise bond, right?

Because I think that can feel threatening. In a similar way to how it can feel threatening, like when the first question I asked you about if you felt worried or fear about not going down this path of the academic discipline, right? We all think there's a path of what a relationship is, and if your partner is doing something different than that, you start to doubt yourself, right?

And some part of me thinks, yeah, how can, that's not right. There must be a way to evolve out of that. Yeah.

Yeah. I should say though that, I mean, this is stating the obvious, but reproductive function is binary. I mean, this is a

That's what I meant. There's a real, it's a reality that has real

consequences that matter.

Yeah, absolutely. And I think that it is very, I mean, I don't want to get too critical, but I have seen, and I've been in forums where There was a clear detachment from reality in describing sexual dynamics very sociologically or culturally, where you start to assign so much weight.

to the forms and practices and traditions and the sort of anthropological reading of things and so on, which is super interesting. And I value a lot and I myself read some things. It's quite fascinating. But when you lose track of the material component of it, then I think it's easy to get very distracted and to get very confused because, there's good reason why the pairwise model in, in romantic relationships is problematic.

I mean, there, there is a very, Obvious. I mean, there are many ways in which it would be selected. Yeah. In both societally, biologically, and so on.

So when you have a family and all that

requires. For sure. And the economic structure that goes into it and everything. But I think what I'm, just to make sure that I come across at least to the audience clearly.

My point here is that there is a clear analogy, fun analogy that you can make between the realm of higher order mathematical research. and the realm of non traditional romantic relationships, consensual romantic relationships that extend the usual pairwise partnership, exclusive pairwise partnership.

And those analogies are both at the formal level of sort of the network structure and also at the societal level of the reactions of practitioners in both fields of mathematicians in one hand and lovers on the other or something, so so that's sort of my main message here that I think is a worthy analogy and I talked to it from direct experience.

I mean, I'm not just observing. I can attest to that. To the reactions. This is not things I read. I mean, this is my own personal anecdotal evidence of people's reaction to, to this kind of things. And yeah, and ultimately there seems to be also an analogy that is kind of more like a cosmic coincidence than anything else, which is that, doing, going beyond binary.

Is a difficult thing. It's not a it's not an obvious thing. And maybe it's difficult because it is it's not being selected for and, if you could say maybe if he's not been selected for then you shouldn't do it. My argument is if it's not been selected for is because we haven't been in the environment that was pressuring us to go into those products.

But if we go into the context where that's the case, then maybe going for these higher order structures might be worth the effort, right? So, and to me, it's been worth the effort, I have to say, in both realms, so.

And, but you're not doing that anymore, the polyamorous?

Yeah. No, I mean this is to me, the way I do relationships is, I mean, my, my transition wasn't, Oh, I was monogamous and then I became polyamorous. My transition was, I hadn't really thought of what doing relationships was. I hadn't matured what it was. And then in my early twenties, I met this partner.

And then we did all this sort of growing and experimenting and so on. And now I think I have a much more. Yeah. Understanding, a much more complete understanding of my own role and how I can contribute to a relationship and so on. I

guess that's what I was trying to get at. Did it teach you about your own limitations or desires or, capabilities, whatever, something like that.

I mean, that was

exactly what it was in some sense. For sure we had fun, we, we had very good times with people we met and it was great, but ultimately. It was a self declared sort of journey of exploration. In the purely personal setting now it was a self declared journey of exploration. I mean, that's how we intended it to go, right? Like we wanted to explore, to grow. We were very sort of relationally and sexually immature in a sense, because we didn't have much experience before we met each other and we wanted to grow in those dimensions while staying together because we really liked each other and loved each other and wanted to be together and so on.

So, in that sense, it really sort of, I would say, It was so long. It lasted for almost eight years, nine years. It mapped out my own persona in some sense. And I, so at the other end, because at the end we had to part ways because we're still very good friends, but she went to a different city. And that was the end of it.

But but the personally, what it taught me. The most important takeaway was that nothing is written anywhere about what I should do. I mean, arguably there are thousands of books written about what I should do, but in my in my list of books that are relevant to live life by, none of them contains instructions about how to do relationships.

So, so yeah it's mostly that is mostly knowing what I can offer in a relationship, how I, what I. Find comfortable what I find, that I need and I can offer. Yeah. It's mostly self knowledge. Boundaries

and limits. And it's. Yeah. In

my case, it was the absence of those.

Yeah. So I think you find them by letting them go and you find them in a different way. You find where you might be, where you want them to be or something like that. In my case, I like going over the edge, where the edge is. Yeah. So,

so, so in my case, I think I'm, I am a, and this goes for all aspects of life.

I am a person of positives, a person of of draws instead of fears or something like that. So, so I define myself All my actions I define in terms of, um, for example, I would never say I have boundaries with partners. I never had, I never explicitly said this is not allowed. I wouldn't go to go.

I wouldn't like to go. I always said I commit to this. We commit to these things to, to hold true. And those things were always desirable objectives or sort of relational places to go to in a sense, right? It's we aspire to be this kind of relationship. It'd be like a more casual connection.

Not very serious to like my main partner that we had like life plans and we wanted to let go for a long time and so on. And so we wanted to plan that out. And to me, the commitment to the plan. Was the core of the relationship it was. So if as long as the commitment to that to those shared goals, shared dreams and so on was being kept, everything else was secondary.

Okay, we'll talk through it and we will adapt in real time. But there was, our principle was always no boundaries and not by position, but it's Because I am a person that goes after positives instead of going away from negatives, right? But just in general, that

sort of goes back to other parts of your life too.

And this honesty, understanding and trying to be clear and honestly kind of, that's the kind of through line I've heard over these hours. Does that make

sense? Absolutely. Yeah. Yeah. That would be a perfect summary of saying yes. Going after the positives going after what's clear the honest feeling of understanding.

There's nothing quite like it for me. And, no, no amount of praise is going to convince me that I understand something better than I actually do. And that was part of why I was, had all my troubles in Cambridge and all the, my, my personal sort of Disquisitions of what am I doing here?

Because people are telling me you're very successful, but I still didn't understand many things. And I saw people around me that didn't understand those things either. And I was like, okay, we're not that successful until we understand those things. So, so yeah the honesty Of assessing oneself.

And even because we've been talking about this personal aspect of relationships for a bit now, like it goes into all this other context where, you know, I just try to be as honest with myself as possible and communicate what I was feeling and needing at all times. And I was always very clearly, okay, these are the positives that I have in life, I have limited amount to live.

I'm going to, Go after those things and I'm going to try and make the most of the energy I have to get to that. Right? So that's

great. Something that helps people probably to hear that. And it connects us to the math, right? Just to end it because math is a pretty honest thing, right?

It's very hard to hide anything with math. So there's some connection there too. And the way that maybe that can scaffold our social personal relations in, at least in that way, it can be a positive, right? To look for clarity of yourself. Of course, you can't like demand this on someone else, but look at your own math in a clear way.

Yeah. Yeah. No, I would say, as I said earlier when I was calling mathematics in a very loose sense, it really means is the rational. Analytical sort of way of communicating and that's certainly something that I live by. I mean, I like to be as clear as possible to the humans around me and manifestation of that is certainly doing mathematics because it's kind of this very pristine way, very sort of narrow channel of communication that You really live the fantasy that you can be completely accurate.

Yeah, and I think it's good we talked about the personal stuff though, because if you just think about that, the math and everything, it sounds very, it doesn't sound sensory, and it doesn't sound rich, and it doesn't sound at all like you're really living life in this full on way. But actually, If you need that, right, like you can't be in a relationship or you can't even with yourself be in a real relationship if you're not trying for that clarity and that actually gives you the freedom, to really sense life and really be involved in it and really let yourself go in a way.

📍 Yeah, absolutely. I think it's a beautiful way

to put it. So thanks. It's been a long conversation. We should probably go. We both have other stuff. But I really enjoyed it. It's you have a lot of great perspective and I'm sure people really appreciate it. So thanks for talking, Carlos.

No, thanks.

Thank you so much, Andrea. It was a real pleasure. I hope it will be a useful conversation for

others. I'm sure it will be. And good luck with all your work. Can't wait to see what comes

next. Yep. I'll be in touch. All right.