#117 - Mandelbrot Set, Fractals & The Quest For A Deeper Reality

Image by Barbara A Lane from Pixabay 

In conversation with Deep & Govind entertaining thoughts on Fractals and the nature of reality. 

Deep is a quantum Computing and UFO researcher, avid participant of Reality and CEO of ReactiveQ, VP AI UAPx.

Govind has interests in computation models of cognition, using fractals to model dynamic systems, logic programming and fractals in number theory.

Projects he is working on:

1. SecureDLT

2. Rabbithole

3. Legal Hackers at UofT Law

This episode was recorded in March and all mentions of COVID-19 are quite irrelevant to today.

 

Episode Transcript and Show Notes:

Download Show Notes ----more----

 

Episode Transcript:

 

SUMMARY KEYWORDS

fractals, mathematics, deep, reality, predict, mandelbrot set, emerges, measurement, physics, hilbert space, similar, model, universe, question, idea, talk, multiverse, super, stock market, measure

SPEAKERS

Pouya LJ, Govind, Deep

 

Pouya LJ  00:17

Okay, now we're live guys. How are you? Good. How are you? Pretty good. Pretty good. Thanks for asking. Going. Ah, we're going to go one by one. So how's it How's it going? How's life going with you? COVID

 

Govind  00:29

life's going good. I'm out in Washington, DC and it's been a while since we did some of these podcasts. So it's good to be back into this.

 

Pouya LJ  00:37

Yeah. Awesome. So yeah, it's been a long while and you have some exciting stuff later on. And in few months to that is going to be out of maybe even sooner. We'll see. Well, we'll just keep it at that. It's gonna be a secret for now. How about you day deep. How's it going?

 

Deep  00:52

I really good man. I'm enjoying the fact that the weather's getting better. I'm out in Toronto for the time being Yeah, I can just like the opportunity to reflect and stay indoors.

 

Pouya LJ  01:07

Awesome. Yeah. Well, so it's a good idea to probably stay indoors. Although it's a very nice weather. It's a little bit cold but it's very sunny here in Toronto. country I don't know. How's the weather in there? Govan in Washington?

 

Govind  01:21

Oh, well, it's it's better than Toronto to start, but it's also a warmer now and the trees are blooming again, because I used to thinking it's spring. So, you know, you know how weather is weather is fractal.

 

Pouya LJ  01:37

Now, why don't you tell us why you mentioned fractals right now.

 

Govind  01:41

Oh, well, because you told me Hey, let's talk about fractals in a podcast. No, I'm joking.

 

Pouya LJ  01:46

Well, that's actually literally why this

 

Govind  01:48

is what this is. But apart from that, well, weather itself is composed of many tiny micro processes that have an emergent macro phenomenon. Right, which is what weather is, the micro phenomenon is like how, how gases move with against each other. Like, like in the atmosphere and pressure differentials that happen due to various like micro conditions like, maybe something gets moved, you know, and then there's something that emerges out of it, which is which is what climate is. So that's kind of really the theme of what fractals are. fractals are something that have that are composed of many self similar pieces. So there's, there's like a large thing, like you're gonna think of it like a square like a square is self similar, because if you cut up a square into four tiny squares, you have each of those squares are just a quarter of the size of the actual square. But then you can you can extend that to something like a cube, which is like you can cut up a square a cube into like, four tinier cubes, each of which is an eighth of the size of the original cube, right? So you can also extend this to something like that. A weird funky curve, you know, like the coast of the coast of Britain, there is a factor by which you can reduce the, the size of the coast of England, and end up with some self similar replicas of the coast of England within the coast of England itself. And that's what's called the fractal dimension.

 

Pouya LJ  03:21

Wow. That's very interesting. And I always have been fascinated by fractals, which you basically give a broad definition of what they are and we're going to talk about them, not just them, but we'll get to a little bit depth and details of these things. Right, so so I'm going to ask deep so what deep Where was the Do you remember the first time you came across these fractals? fractals like as like, as general? Yeah. As a concept. Yes. So I would say I was in either grade eight or grade nine. Okay, you were early bloomer. I was. It was a little Whatever the leader later for me,

 

Deep  04:02

like, I understood the deepest mathematical aspects, but I knew what they were. I love them. So like a quick, like 10 second background, I was like a, I was a huge user of the internet, like from an early age. I'm sure both of you were to like, Haha, yeah. Yeah, that's what it seems like That's out of the question. So, um, so yeah, but I So, apart from playing a lot of runes game, I used to troll around on physics forums a lot like, around like grade seven, I got really obsessed with it. And through that, like these researches, just reading people's thoughts, eventually I came across fractals, so that was around grade eight, grade nine. It's amazing

 

Pouya LJ  04:43

now, for people who are like, well, what the fuck are these guys talking about? Why is it so beautiful or amazing or whatever? We're gonna just definitely put these in the show notes. Just go look at us on pictures, google it yourself, whatever is more accessible to you. But there is some beauty in these and the fact that we perceive them. As beautiful as it could actually be, has have some meaning behind it. I don't know. Have you have any of you thought about that? Why do we think of these things as kinda like beautiful or mesmerizing? Which I do and I know a lot of you do.

 

Govind  05:13

Well, I can start that one off because I think just the hyper fine structure and symmetries to fit is almost incomprehensible, right? There's like, no matter where you look in the in a fractal like a canonical fractal is the Mandelbrot set, which I'm sure we can include that in the show notes. If you look at it, and you stare into it, there's even some videos on YouTube of of like zooms into the Mandelbrot set. It's just no matter where you see there's just like these hyper structural patterns that are just so symmetric and so perfect that it's it's like hard to comprehend something like that can exist, right? I think I think that's what makes it seem so beautiful. In fact, well to answer your earlier question of where you encounter the fractals first and you ask the deep but I was raised as a Hindu. And my, my mom always used to draw these little pattern things out of flowers out of rice, flour, wheat flour, whatever. And this is like a big thing in Hindu culture. And I'm sure it is in other cultures too, right? Like, you just have fractals ingrained within us something that's beautiful. Yeah, you're

 

Pouya LJ  06:21

interesting. Actually, that's true. If you look at culturally, you can see these patterns emerging in a lot of cultures as an active components of, I don't know, symbology or whatever. Now let's get a little bit deeper. So about I don't I want to say about two years ago, or one and a half, or maybe one. Anyways, what somewhere between one or two years ago, you came to me with the notion of these fractals and you you were working on something specific and you mentioned that I'm doing this do you want to jump in we're well, deep is going to jump in as well. That's actually quite interesting. Do you want to Tell us a backstory of what that whole thing was and how you came to contact with it.

 

Govind  07:05

Yeah, for sure. That was the Mandelbrot set again, a little bit of foreshadowing here. And the project was to do machine learning on the on the Mandelbrot set and see if we could use something like saying you will network to learn the layers to learn the different resolutions of a Mandelbrot set and see if you can actually predict what a Mandelbrot set zoomed in is going to look like. Based on the training data. I thought that would be super fascinating just because we can that gives us more insight into something that's not really well understood in mathematics, which is fractals, right? Especially the Mandelbrot set. It's a class of functions known as iterative functions. And those produce very strange behavior. Because, well, for one, the Mandelbrot set is just composed of the root x squared plus C in the complex domain without wanting to get too technical and in the weeds, it's a pretty simple equation that generates something just so chaotic, which is a common theme in modern Mathematics and Computer Science or something very simple, like a very simple rule can create something so complex, like, infinitely complex even.

 

Pouya LJ  08:19

Yeah, no, that's, that's great. And then we jumped in, we started working on some aspects of this, this project, we were struggling with so many so much details that are redundant here. But for the for the, for the fun of it, we had trouble computing, large amount of basically large resolutions. So when you were trying to compute large subset of these numbers, it was becoming very time consuming. And we had a lot of those challenges which was, which was fun, very rigorous, and, and just just mentioning that as somebody who's not if you're listening and you're not familiar with these, there's like a lot of heartache and headache and never sweat goes into these things just for the appreciation part of it. But eventually, they, the beauty emerges. And that's where you're rewarded. And you're like, Ah, it's totally worth my time. And that's how I look at it at least now. Okay, so at the beginning, we, we started generating these so deep. So I'm going to go to the application a little bit. Each of you had some aspect of how you can apply us. So the question is, why do we even care, right? Why are they important? So each of you had an application in the real world for these for these patterns. Now, I'm going to start with you you had something I think in in fluid dynamics.

 

Deep  09:43

I yeah, that's right. So with fluid dynamics, there's actually different applications that we can use fractals for. My favorite one is more of like, it's more of a meta statement of how we can use practicals in physics in general. So not just fluid dynamics, but other times. Which is the idea of taking the very strict approach that if we're to study the universe and the physicality of the universe, then then the rules are the same no matter where you look. So it's just a matter of knowing where you are. And that fractal layer, right? The depth, that infinite recursion, knowing where you are in there is the question that we're trying to solve at any given time. So one example that will give to you is that consider the common problem of classical physics and quantum physics that are always brought up how the world when we zoom away, we aren't looking at each individual particle. It follows this classical rule, right? All these different subsets of classical physics instead. And but when you zoom in enough and you zoom into the universe's fractal real life fractal, you see that different rules apply quantum mechanics applies instead. So I like the idea When we take the fluid dynamics example of applying the fractal mentality to whatever object it is that we're modeling. So earlier, I brought up an example when we were discussing offline of the plane where different parts of the plane are experiencing different physics that we're interested in modeling at the surface layer at the boundary layer, which is the sub couple millimeters thin layer at the surface of the craft, and forms when you're at hypersonic speed. So five times the speed of sound when you're traveling at that layer or more, so it's a place where eventually air goes from very still in calm and fluids and the gases to extremely turbulent. And in doing so, you have all this chemistry that you want to predict, like how will the change in the temperature of the air here and the chemistry of the actual atmosphere affects that The let's say the paint or the heat of the craft at the surface layer. But then if you back up and you want to look at the physics of the shockwaves, which is around the craft instead, that's following slightly different physics. We're not interested in the chemistry anymore. Yet, when you take a step back further and look at the whole plane, it is just one system that we're that is just unique and unified that we're interested in. So it makes sense to apply fractal theory in that respect. Yeah.

 

Pouya LJ  12:32

Cool. And so Govan you have some application in cryptography, I believe.

 

Govind  12:40

Yeah, that's cryptography. But um, well, okay. So in the in cryptography, there's the idea of private and public key pairs. So there's the one idea that seems interesting to me, which I think has been explored in academic literature. albick not much is being able To use different uses of scale invariance properties of fractals to generate, generate a key pair where your scale for those of you that are familiar with private and public keys and encryption using those or rather unfamiliar, a public key is what is presented to the world. So you can lock up your, your data or your information that is secret or using your public key. That is your private key. And then that can be used against your public key to generate to regain that information. So think of it as like a lockbox where you lock it with one of the keys and the other key can open it again. So typically, this is done using using large prime numbers like RSA, RSA encryption, but using fractals The idea is that you can you can encode the like say one Part of the a fractal like if you're thinking of the Mandelbrot set, you can think of the big bowl of the Mandelbrot set. And you can encode information with that. And then you can transform your scale to find another one of the big bugs within the Mandelbrot set, which we know is possible, right? And then that the transformation that you used to get to that point would be your private key. Well, yeah, this is getting like pretty complicated. But now it's supposed to be easy, isn't it?

 

Pouya LJ  14:29

Exactly. I mean, I'm happy. First of all, I'm happy that complicated but no

 

Deep  14:34

easy stuff has been done. So

 

Pouya LJ  14:37

now, but it will also include some people who are just listening to this, we will include more details stuff in the show notes. So what Govind is basically explaining with some graphs or or explanation will make more sense to you. So continue, please.

 

Govind  14:52

Yeah, and I also wanted to talk about less complicated while still pretty complicated application. In which is the stock market? Well, the idea of using fat or the stock market is by no means new. In fact, Renoir Mandelbrot, the namesake of the Mandelbrot set that has been repeated ad nauseum in this podcast is, is famously, like one of the notable things he did was try to predict the fractal dimension of various indices in the stock market. This is a technique that's still used and widely studied in, in, in modern mathematical finance. Yes, that's, that's definitely a very, you know, out there application of fractals, right. You mentioned

 

Pouya LJ  15:39

before, briefly the fractal dimension, but can you reiterate what that is?

 

Govind  15:45

Yeah, for sure. So just how, if you're able to, if you take a square and you're able to cut it up into four pieces, and each of those four pieces is still a square, right? It's a square but like it's a scaled down version of a square, it's like magnified a little. It's like A quarter of the size, right? So if you, you can abstract that concept to a cube. But then you can also take that to like the jagad. Coast of the United Kingdom, right like this. This sounds like it's coming out of left field. But just Just think about it like the coast of the United Kingdom is like a bunch of squiggles, a lot of squiggles. So if you take that, and then you try to find some little tiny squiggle within that big squiggle that resembles the bigger squiggle a lot. It is basically a scaled down version of the bigger squiggle, right?

 

Pouya LJ  16:34

Like the smaller cubes and the bigger cube basically.

 

Govind  16:37

Yeah, exactly. That's the analogy, right? So we're in four squares, it's two dimensions, four cubes. It's like three dimensions. You can you can have like, weird like, like rational number dimensions, where you have like two thirds of a dimension like a 1.6 dimension. So that's the real intuition behind practice. To fully understand it is the fact that it's you're not working with like, dimensions that are easy anymore. You're working with dimensions that are just weird, completely weird, right? So how does

 

Pouya LJ  17:09

that non natural number perfect dimensions work like the 1.6.

 

Govind  17:16

So it's exactly what I what I explained earlier. So maybe in the show notes, we can include the definition of a fractal dimension, which is the number of self similar pieces within the within the curve or the object. So again, in a square, you can you can cut up a square into four pieces, and then the number of self similar pieces is four, and then you can divided by the magnification factor, which is which is a quarter.

 

Pouya LJ  17:41

So I see Okay, fair enough.

 

Govind  17:43

That's that's literally how you get it. But if you use a log, you have to use the log function. So it's log of the number of salsola pieces divided by the log of the magnification factor. If you're being precise.

 

Pouya LJ  17:56

Yeah, yeah, no, I got it. Okay. So so you remember So these are useful also in. So when you mentioned markets, so are you talking about predicting the markets?

 

Govind  18:08

Yes, exactly. To give you a little bit of an explanation of how this could work, if you see the stock market curve, maybe in the show notes, we can put the Bitcoin curve because it's, it's very easy to see these kind of self similar shapes. Okay. You can see how there's like a huge peak, and then it goes down, and then there's a huge peak again, and then it goes down. So intuitively, it is kind of self similar right there. There are these chunks where you like, again, if you think of it as a big squiggle, there's this tiny squiggle where it goes all the way up, and then it goes down. Right? It's like it's kind of like a sine wave. It's like, it's like a curve that goes in it reaches itself again. So it's kind of self similar in a sense.

 

Pouya LJ  18:51

Would you agree with that? No. Yeah,

 

Govind  18:53

yeah. So the idea is that you would use the point where it seems to match Like one of the ends of the curve, and then you can say, okay, based on my fractal model of the stock market, it looks like it's going to repeat at this point. And then you can, you know, make your investment based on that decision.

 

Pouya LJ  19:13

Right. And the rationale is that so, so I don't know if we discussed the model that our project is creating the machine learning model on the when we were online or offline, but did we mention it online?

 

Govind  19:28

I'm not quite sure actually. Okay, let's

 

Pouya LJ  19:30

reiterate. No, otherwise, let's go for it. Okay, so So what are we doing in our project basically.

 

Govind  19:38

So our project is to better understand the Mandelbrot set and how we can apply it for for use cases such as, I think the basic first step is to actually just see what happens can we actually predict layers of the Mandelbrot set right? Or is it gonna get hairy is something like is the best thing Yeah, that we have currently not able to learn the Mandelbrot set or like fractals in general.

 

Pouya LJ  20:06

You know, I think, what is it? Guess? If you had to take a guess Yes or no? Uh, you can you can explain why briefly by one yes or no.

 

Govind  20:16

My disclaimers? I'm not sure, of course. But I want to say no,

 

Pouya LJ  20:20

because I can't predict that's what you're saying.

 

Govind  20:23

Yeah, just because it's so computationally intensive. That I think there's something deeper mathematically hidden within these, these curves that simple statistics will not be able to help us get there.

 

Pouya LJ  20:40

Okay, what do you think the same question? Yeah,

 

Deep  20:43

I couldn't agree more. I think what we'll see if we're lucky is some kind of like Kwazii you know, like a five year old trying to recreate a drawing of a dinosaur like we might get something of that kind, but to truly capture the underlying mathematics or current regime of machine learning is just not there yet. Okay,

 

Pouya LJ  21:03

fair enough. Now,

 

Govind  21:05

I just want to see if I if I'm wrong. Hey, like, I think that'd be pretty cool. That in itself was a good discovery.

 

Pouya LJ  21:12

Yeah, no, I'm gonna be rooting for you to be wrong, honestly. So so don't worry about it. If your rock no but so as we're so basically as So, if we do train some AI that looks at these, these layers and tries to predict them and say they're successful now. Excuse me, how do we so it seems that if you're able to predict the the market, the economical market, you should be able to predict any anything else with any kind of self replication or self similarity. Would you agree with that?

 

Govind  21:54

Yeah, because, well, if we do predict the stock market successfully, well apart from being insane Rich, we also have predicted human behavior because that's kind of the underlying, you know, that's that's how the stock market works, right? Like, that's how economic models work.

 

Pouya LJ  22:10

And do you

 

Deep  22:13

need your to get a two for one deal? That's all I want to say. Haha.

 

Pouya LJ  22:17

No, actually, I was gonna ask you further. Do you have any other similar applications in your mind that is, like stop for you there or do you? I'm talking too deep actually. Okay. Do you think it has potential to go further in terms of what you can predict with these things? Do you have any examples?

 

Deep  22:34

Yeah, so one thing that and again, it's maybe less so about predictability, but we'll see is let's go back to quickly quantum mechanics and the fundamentals. So wait, let's so when we look at a system and we want to define the measurables of the system, what we're really saying is that this system has these kinds of measurements we can make and these are the five values that you can measure the system to be in. And that's all defined in the wave function, right? It's all encoded in there. And so you'll never, in theory, measure anything outside of that wave function. The wave function is supposed to contain everything about a system and the measurements you can make. So if you want to, but then if you dig a little bit deeper, you see that the actual definition of a measurable is that the value maps to the eigenvalue which maps to the eigenvector of the Hermitian operator, which is acting on a quantum state. So let's say that I have some sort of qubit, superposition or some sort of system, forget a qubit, any system physical system that's in a quantum superposition and I want to make a measurement on it. The way that I would define the state of that system is using Dirac notation. It would be a vector in a Hilbert space. Sometimes it's finite dimensional, sometimes infinite dimensional and there are different kinds of Can you super quickly explain what Hilbert spaces the Hilbert spaces, think of it as a generalized Euclidean space. So it's supposed to represent a more abstract vectors like complex vectors, while it also defining certain functions that the normal Euclidean space does not, I believe that includes the inner product. There's a specific kind that you can do quantum mechanics. So beyond that, the the whole idea though, is to keep that idea of conserve that concept of Euclidean spaces just at much higher dimensions, because keep in mind, we're representing quantum states in those dimensions where your, your actual vector is represented by a complex number, or it can be like your, the elements of your vector. So and so the more let's say entangled systems, you have the higher dimension, Hilbert space you're dealing with. So in the quantum computing regime, if you take, let's say, three cubits and you entangle them, then you're dealing with a Hilbert space, that's two to the three or eight dimensions large, and so on and so forth. So, so yeah. Does that make sense? So like the Hilbert space is really just a fancy Euclidean. Awesome. Great. So So and also, one thing about the Hilbert space is that it lets you using the vectors you can represent superpositions, which is insane, right? That's what we really care about. And so we so going back to the system that we haven't measured yet, it will be represented by this state function or this vector in the Hilbert space, right, let's say it's in a superposition. And the vector accurately reflects that. Then the measurements the possible values that we can measure in that system depends solely on the operator, the measurement operator that we're applying to that quantum state. So if we Apply, let's see your position operator where we want to measure the position, what it's going to do is it's going to apply that operator to the quantum state, and map all the possible states of that quantum state to the possible eigen states that consists of that operator that we just applied it to. So that's how you're able to kind of force these values, right? Of like measurement and, and all that stuff. And you know, you're constantly doing this mapping, like you either did a unitary action, which means you did disturber make a measurement to the system, or you did a measurement action. Now, why is that related to fractal theory? Like why am I rambling about the specifics because of the 10 Martini problem. And so the 10 Martini problem is looking at addressing quantum mechanics and operator logic and the spectrum of observables and all the mathematics that goes into that, right so now, rather than having a finite number of observable What happens in vivo continuous model? So what they deal with one thing that xR t looks at is the application of fractal theory applied to this, the problems that we come up with, and we find it in measurement, like quantum measurement and operator theory and operator logic.

 

Pouya LJ  27:19

Right. Right. And and for those who are not familiar with the martini problem, can you quickly give a gist of it?

 

Deep  27:27

So I'm gonna divert that to go, Vincent. All right. Yeah, he was the one who had sent it to me, but I have my own interpretation for what it's worth.

 

Pouya LJ  27:36

Okay, so go and give it give a brief on the paper description of what it is and then deep you can interpret all you want.

 

Govind  27:46

I have to confess I don't fully remember it.

 

Pouya LJ  27:52

So we'll put it in the show notes if you don't remember.

 

Deep  27:56

Yeah, yeah, yeah, we can. So all I want To say about it was that is the fact that, like, for me, it was the spectrum of the matter you I can never pronounce his name but like Matthew operator, they found that it's a cantor set for all nonzero values, right for all these, the coupling of all irrational frequencies. That's like the formal definition. What they found, and I think it's like, that's why it diverted to go in because of the whole idea of the cantor set showing up. But um, yeah, I think what we should do is, it's almost worth talking about in a different podcast, but let's just go knows for now, yeah, no,

 

Pouya LJ  28:39

that's good. Yeah, I don't want to, like confuse people, like a, like, you know, like, we need to be super rigorous in what we're saying. So you know, okay, so we actually do have plans to do another in depth podcast so we can mention the details of the 10 Martini problem

 

Deep  28:57

would be the perfect place to do it because like we're we're learning really getting into the deepest parts of like, this stuff is not

 

Govind  29:03

easy to talk about. And then with quantum and well, there's of course, like the whole cliche Fineman quote of nobody in quantum really knows what they're doing what quantum is. They don't understand it.

 

Deep  29:13

Yeah, for good reason. Like I was actually what we were talking about with like the quantum theory with free join. We'll talk about that more after but yeah, well,

 

Govind  29:21

one fun fact about the 10 Martini problem is the guy who came up with it. He said he'll give he'll buy 10 martinis for someone who can solve the problem.

 

Deep  29:31

Oh, that's amazing.

 

Govind  29:33

Yeah. Another fun fact is the solution was given by a fields medalists from, I think like the middle of last decade. I think somewhere on 2015 or 2012. I turn Villa and he's the one who actually discovered the fractal implication for the the problem that was you know, didn't seem to relate to fractals at all, which shows how deeply embedded fractals are. Mathematics. Yes, again, I think this this, this scan should be covered in a separate podcast just because you know, like, we don't want too many icebergs floating around here. Yeah, no,

 

Pouya LJ  30:09

no, I agree. And they will do that. So for now, anybody who is wondering what, what the heck this thing is just look at the show notes. You'll get the idea but Okay, now, if any, if you don't have any specific like nooks and crannies details, Oh, actually, let's before that. Do you want to talk about where the project is going in the future that what are we try aspiring to essentially so right now we're basically developing the training these models to see whether we are we are able to train them and they are able to predict rather. So what's next?

 

Govind  30:45

Well, we have mind a an actual fuck ton of data. I'm not kidding. Nearly one terabyte of data. That's just sitting on a drive somewhere. The next step is to actually do the machine learning, which we've already kind of kicked off, we have our general model architecture that is derived by beak over here. And we need to actually do some batch machine learning over just tons of cross sections of data. Because we have such a huge data set. I live in safe if there's anyone listening who would like to join, you know, just shoot, shoot us a message, and we'd be happy to have you on that project.

 

Pouya LJ  31:23

Yeah, absolutely. It's a it's a completely open. So we're looking forward to hear from different people. Yeah,

 

Govind  31:28

it's open source. And it's a it's a really interesting problem for for machine learning in general. It's a very cool role.

 

Pouya LJ  31:35

Certainly. Now, if you don't if either of you don't have any specific thing to our project and these applications, I want to abstract out and talk about fractals a little bit broadly. You have anything to add at this point? I know I'm good. Okay. No. So what I asked you these before any steps into more philosophical realm a little bit, but again, as we talked in the fractals seem to be completely available, like existing in the background of the entire universe. If you zoom in, in any specific part, you can see them when you zoom out, you can keep seeing them, again, like galaxies that they're essentially these. So, in a sense fractals themselves. But then even even if you zoom out further, you can see super close super clusters or other clusters of galaxies that again, are self similar, fractal in a sense, so why does it why in Europeans does this fractal behavior exist? It seems inherent or maybe even fundamental in the universe, or maybe it's American that actually let's talk about that. Is that religion is a fundamental Yeah.

 

Govind  32:50

A few years ago, I remember there was a picture floating on the Internet of something like what you said like a cluster of galaxies, and also compared with a protein picture of a protein which which has, you know, like proteins look all squiggly and weird and stuff. Yeah. And most of my friends that I like and then there was I think inevitably it was some relation to how like intelligent design and all that stuff was there, which is not the focus of what I'm trying to say is this Mr as complete bullshit, but, you know, like, that's kind of what I'm trying to get at with the deep embedded nature of fractals and everything. I think well, since in mathematics, we generally deal with a lot of spaces right like I mean Hilbert spaces an example of one there are spaces of fractals themselves, right? spaces are fractals being in the complex plane, you can you can actually create, like use iterative functions on every single point of the of the complex plane and you end up with a unique fractal for each of those points. And those points are known as Julia sets. So each of those, those those fractals are called Julia sets. And what's really interesting is if you put those As a side note, if you arrange all those Giulia sets into different points, what emerges out of that is a Mandelbrot set. And that can we can add on the show notes. That's just that's just a really wacky, cool thing in mathematics. But I think it's, it goes to that, like, I mean, there is there's this debate in mathematics of whether mathematics model is just the best approximation of nature or on the on one side of the coin. And the other side of the coin is, well, mathematics is nature. And we're just trying to understand nature better by understanding mathematics better. So it's a I think it does come down to this, this, this two sided coin and this debate that's always going back and forth. But either way, I think nature is just really well approximated by fractals, I think it's the these like, Who's to say maybe we can even come up with some kind of super fine structure that we can use to approximate every single curve that we ever see. To an infinite degree, like now we can use calculus and we can get there to, to to a similar degree, but not quite there, which I'm sure we can explore at a later conversation. But I think I think fractals might actually help us get there.

 

Pouya LJ  35:16

Okay, and as to the question of whether in your I mean, I know it's purely an assumption, but do you think they seem to be more emergent or fundamental at this point?

 

Govind  35:28

I think it's a it's emergent like, because, again, most of these things have to do with I mean, it's always like, I mean, even the definition of a fractal dimension is is the number of self similar items that are there within an item and then their magnification factor, right. So like the, you start with the most basic unit and then the fractal emerges out of it, right? You have like you start with like this super tiny self similar, like seed, and then the, the rest of the fractal emerges out of the seat by the end and the way you operate it right, the way you magnify it. And the way you arrange it. And to make that clear, think of again a square and cutting up a square into 444 pieces. And then you see a bigger square emerge out of that, right? Your unit is a square. So it's kind of like that. But yeah, you don't know. Like, as with most of these emergent phenomena, you don't know where one ends and the other begins, right? Yeah, no,

 

Pouya LJ  36:19

that's fair. How about you? Did you have any thoughts on the matter?

 

Deep  36:24

Yeah. I mean, I agree with Govan, that it's fact matter is we're we're touching the deepest, one of the deepest questions about nature, which is, is math discovered or isn't invented, right. So like, so but that being said, like I've always, not always like recently concluded that. Going back to like the definition of superposition, I really like what it says about reality. Because when something's in a superposition of, let's say, two states, it's never saying that it's in either that state or the other state or both states or neither the states, it's saying it's in a superposition. Which is, which means that we can't physically say anything about its current state in any logical manner. That makes sense. But when you measure that superposition, you might get one or the other state, depending on the probability and what kind of superposition was so. So you'll get different answers, varying answers every time you make a measurement. And I feel like that's what happens with this. Of that is what's happening with this question of the dualistic sort of divide we take with ascertaining whether the universe is mathematical or whether we invented because it might not be either or it might just be a superposition of the two. So sometimes, factor like behavior we observe in the universe is truly just emergent. Sometimes it's the other way around. Maybe that's what I think.

 

Pouya LJ  37:51

Fair enough. Now, I want to throw out two other concepts that we're going to talk about in detail later, but I want your feedback like a short feedback. At this point and mentioning all of these mathematics being either developed or discovered or invented or discovered now, so I'm not sure if this was Lee Smolin, but I believe it was that was talking about possibly the laws of physics and the laws of the universe being being not constant, rather not fundamental right and evolving. And I again, I'm sorry if I'm misquoting him for somebody else, but so what are your thoughts on that?

 

Deep  38:38

So I love that because I love that. We're still thinking about that, because it's important for you to question right, but like, okay, I would like to know if the physics, you know, right outside of the Hubble bubble completely changes, right? That's important to know. So, that being said, so I believe the term is isotropic and anisotropic. Right. So like, So when something is added to tropic just for the listeners, what that means is that when you measure it from different, it likes physical angles or just different ways it has different properties. So the measurement, the type of measurement you make affects the outcome. And whereas with isotropic no matter where you measure it, or how you measure it, you will get the same result. So, physical example is, let's say like I take a sphere, and it's a perfectly like cut, you know, Diamond sphere. And if I wanted to measure, like, let's say the diffraction at a specific point on the sphere, it's going to be the same angle wherever I go, right? So that makes that property diffraction, in this case, an isotopic property of that diamond. Whereas with and so when you look at the universe, we're constantly asking you're likely Smolin and others is the universe isotropically When you look far enough, or is it anisotropic, where we have different physics when you measure it from a different place? And I think it's inevitably the latter. Even if it's not like, in our universe where we experience different laws of physics, it has to be the case. I think that there are other laws of physics out there. Because like, the fact that we exist means almost for sure that reality has existed before. And it does, like in other ways, but again, that's just another guess.

 

Pouya LJ  40:31

Right? Yeah. First, how about you? What are your thoughts on this? Oh, well, it's uh,

 

Govind  40:40

yeah, it's, I guess it's kind of this is regarding the invention versus discovery right of mathematics.

 

Pouya LJ  40:47

I think we I mean, so if we tend to accept that the laws of the universe are not fixed, evolving, or rather existing completely differently in a different unit. Reverse like now, will the same math explained both of them? Or rather, you have to modify it. So that maybe speaks to if you have to modify it, or there's a different math this might speak to, it's being invented to explain something rather than discovered. Or you can say, Well, that was different law. So it's mathematics. But they're the two different maps because they're two different laws. So in that sense, I want I'm thinking about it.

 

Govind  41:29

Well, I think, Well, for me, the core of mathematics has always been logic and logical inference. So if a different math had a different conception of logical inference, or maybe didn't even have logic at all, I think it would really be inconceivable for me, almost literally, I don't think I'd be able to conceive of a mathematics that's not I mean, maybe you can think of it as having different rules of Like rules of truth and assigning truth assignments to statements like or assumptions right, because most, most like I mean all models in mathematics are axiomatic you know, you have set theory, which has the set theory axioms, probability theory has the probability theory axioms and then you derive the theorems from all of them, right. That that is kind of the the heart of mathematics in my opinion, at least, if we if there is a different kind of mathematics, I'm not sure what would follow, but, that aside, I think, what the purpose of mathematics is, at least for the broad case of most humans who just want to you know, find out how the world works, and manipulate it according to what we want to do. I think, any form of mathematics would, would would serve that purpose, give some kind of objective script on causality objective as objective as possible. script on how we can reliably understand and abstractly understand and manipulate how the world works.

 

Pouya LJ  43:07

Okay? All right, that's fair now. So I'm going to throw a different question. Now if if the laws of physics, universe do in fact, differ in different either different times, or different realms or different universes, whatever you want to call them, would you think would you say either of you in throwing it out there? The same mathematics that we have can construct similar? I'm not like my details like what you said, actually, Matt. So maybe with a different set of axioms, well, essentially with the same logic constructor, we can come up or we can

 

Govind  43:39

not complete care.

 

Pouya LJ  43:41

Exactly. Can we can we describe those set of rules with but with the same basics of mathematics as we know it today? I know it's incomplete, but I'm just talking about philosophically speaking.

 

Deep  43:52

Hmm. So let's look at the idea of different infinites first, because

 

Govind  43:58

when we're done Good one.

 

Deep  44:01

So, so think about the multiverse for a second. And you know how there's different kinds of infinite, right? Like from zero to infinity, and just the whole numbers, and then all the integers and all the rationals. And all that stuff in the set keeps getting bigger and bigger, right? So think back to the multiverse. We don't know what kind of infinite it is. We don't know how large that set of infinite multiverses might be. And we don't know how large the number of people, or we also obviously don't know the anthropic principle, but we also don't know the number of inhabitants or life forms that exist out there in the multiverse. And that matters, because what if the Infinity for the multiverse is larger than the infinity of sentient beings out there in the multiverse? That means that you have leftover multiverses right that aren't inhabited, then in that case, if we're going to take physics as we approach it from the measurement, Problem approach, then we have no way of saying that there even is a physics in those multiverses where there is no one to make measurement. So my answer is that we would need a different kind of math and different kind of physics to address the physics of other multiverses that don't floor

 

Govind  45:23

Yeah, I mean, I think it's good that we are we're at least someone who's talking about these these these questions really, because it's, it's it just gets so hard to even talk about these because you you need to be at the highest level of abstraction at so many different fields. Stephen, this is kind of an emerging field like even true multiverses right.

 

Deep  45:44

Yeah, it totally is, like we, I feel that this century in this Millennium general will be a millennia of probing the multiverse and empirically proving it and just going farther and farther even trying to make like portals and ways to go, you know, travel until the multiverses I think we will do that at some point. Not in our lifetime for sure. But I eventually.

 

Govind  46:06

Yeah, I mean, let's hope it's in our lifetime. That'd be pretty cool.

 

Deep  46:09

Yeah. Make it happen. Yeah.

 

Govind  46:12

And I hope fractals will get us there.

 

Deep  46:16

Totally.

 

Pouya LJ  46:17

Now another thing that I want to throw at you, so two things. I mean, this is again, we're coming to the end of the show. So I want to basically make it very short, but we're going to talk about it in depth later on. But that is the I think I shared the book with you. I don't know if you have the author in front of you because I am blanking on his name. But the the book that he has is the case against reality of Donald Hoffman. Hoffman. So So once again, I I didn't read the entire book yet, but based on me hearing him talk in other people's talk about his work. Now his point of view, is that okay, reality as we come to define it, however you want to define it. It's not really Really, really the deepest of the realities that you can possibly think of. And it's the it's evolutionary, with. So this is what his saying it would be evolutionary, against our interest to actually understand reality as purity, because then we couldn't function in the world as we do. So for instance, he gives the analogy of computers and let's say you're moving objects than on your desktop to different folders to the recycle bin, whatever. And now, this is not literally what is happening at the low level of the computers. But it's a good approximation for us to understand and and us to do our things in the computer. Now, what are your thoughts on that? either of you can go first, maybe?

 

Deep  47:47

Sure. So, first of all, like I really like the idea that he's taking the evolutionary approach of like, okay, maybe it's not even worth knowing the true nature of reality because maybe That's why we don't have like natural intuition for quantum mechanics. Right? It doesn't make sense to us. It's literally literally not logical, the way that it behaves and simplifications for sometimes. So, I wonder, though, like, and is it? It depends, but I wonder if we can like, train the next generation of, let's say, children to have a different intuition. Right. And to have a better deeper understanding of reality. Would Hoffman consider that as going against? What is in our evolutionary benefit? Right.

 

Pouya LJ  48:34

Yeah. Right. So based on what I understand of him, I don't want to butcher his point of view, obviously, but this is just my interpretation of what he's saying. And that is, well, maybe not in one generation. And it doesn't mean that we cannot develop tools that help us understand the nature but that's not so that's not really natural to us, but so we have to put a lot of work to actually duck deep so he's not imposing that it's always like it, like, absolutely impossible. And there's no way we ever can do this. That's not what he's saying. But he's saying maybe maybe that's the case. But I'm more optimistic. And I think we can like develop tools like we have to both science to further understand the reality like at least closer realities of the universe rather than some further approximation of them and get keep getting closer and perhaps getting to the, to the, to the thing, whatever that is, but, but I don't think he's just going to accept the training of a next generation as enough of a step. Awesome.

 

Deep  49:39

Yeah, that's good.

 

Pouya LJ  49:40

Yeah, you go and what do you what do you think about this whole

 

Govind  49:44

thing denying of reality, okay. So

 

Pouya LJ  49:48

so his book is called the case against reality in that okay, like, actually, I don't know why he names that book. As it as he did again, because I didn't read the entire book. I've mostly heard him talk about that. The book. So it's not a fair assessment, but essentially so. So do you think there is a complete like, again, going back to the analogy of the computer, so when you're moving icons on the folder, two folders and from the folders, that's way far from what is actually happening, and there's a bunch of electrons moving around, and there's nothing, you have no understanding of those electrons when you're moving into computers. So do you think we're stopped Far from it? absolute reality, if you will?

 

Govind  50:28

Well, I mean, this is this is a question of philosophy has been trying to address this specifically metaphysics for like, hundreds, thousands of years, right? Where we started out with, like all our ancient, like rationalist philosophy from Aristotle. And then we end up with empiricism. And then we have Khan who's like, hey, why not both, you know, I don't want to go too deep in that in that rabbit hole. But, um, well, the fact of the matter I think, a good philosopher to use for this discussion is Charles Sanders. appears you know, if you take if you take, you know, the blind spot in your right, right? Yep, like we got a spot where I think the optic nerve passes through. So it seems like there's like I mean, when you put something there just doesn't show what that what that is you can directly look at anything that's in there. Well, what happens is that your your eye kind of fills up the gap with something else like I mean, the experiment that Charles Sanders fear said is like you take a little Penny, and then you You look really you put it on a piece of paper, and you look really close at the penny until it goes into your blind spot. Your I won't even look at process depending it'll just it'll fill up the gap with the paper that's around it. So I mean, a lot of reality is just our cognition being projected onto it. But that isn't to say that we are we're, you know, we're tripping on some you know, acid reality. Completely. I think most of what our body does is to just enhance our experience and make sure that we're always alive and aware of what's going on. I'm making an evolutionary argument, I guess, in this case, yeah. But to say that we're separated to such an extreme degree from the actual objective reality seems a bit of a stretch to me.

 

Pouya LJ  52:24

Mm hmm. Okay, cool. We discussed this definitely further. Because again, it's a whole topic on its own. We can separate these. I just wanted to throw them out there because they're quite related in this in this realm. What we're talking about all of them can come together, essentially. Yeah. So thanks, guys. This was awesome. We are going to definitely deep dig deep in all of these subjects that we talked about 10 Martini problem and what do you got these two that I recently introduced and basically bring everything together at some point. If you have any final words, go for it. Otherwise, I think we can adjourn here.

 

Govind  53:00

Well, I'll say that I'm, I'm very excited for the fractal project, and to see what kind of models we can come up with, and we'll be sure to keep you guys posted on what we make of it.

 

Pouya LJ  53:13

Awesome, YouTube.

 

Deep  53:15

I just want to make one final comment. And also Yeah, I echo Goldman's thoughts. I think this project is going to be super cool. It's going to reveal a lot of things about reality that we all care about. But speaking of reality, my final thought was that we definitely need to get better with and we'll talk about it more next time. But, um, so one of the best philosophers of all time and especially of the 20th century, who's also logician his name was Ludwig Wittgenstein. He had a bunch of he made a couple of breakthroughs in philosophy and logic, and one of the ones that he did in philosophy, like the general idea, came down to him showing debunking the use of language and how we don't use it properly. And even when we do, it still isn't good enough in the way that we use it for what we are trying to approach and accomplish and tackle. So he like really emphasized the use of language. And when it comes to the idea of reality and objective reality and how far we are, we definitely need to agree on definitions better and have super precise, rigorous, you know, wide varying definitions of reality and just super nuanced looks on what we mean when we say that.

 

Pouya LJ  54:32

I couldn't agree more. That was actually well said and awesome. Alright guys, thank you

 

Deep  54:37

for the awesome chat, by the way, very engaging.

 

Pouya LJ  54:39

Thank you. Yeah, definitely. I always enjoy having a chat with you too. It's amazing, either online or offline doesn't matter. I hope our listeners will enjoy again we picked this up later with more depth and until later episode, have a good day.