Power Law and Bitcoin's Growth

Hi everyone, welcome back to Stephan Livera podcast brought to you by Bold. So for American listeners, you can go to getbold.io, you can buy Bitcoin there, and Bold has a vault where you can use your own two of three multisig vault where you hold two keys to store your Bitcoin. So that's getbold.io. Now joining me today, we're gonna be talking about the power law With the, let's say, the founder or the creator, let's say, or the first person to kind of properly make this association, Giovanni Santostasi. So, Giovanni, welcome to the show. Thank you very

much

to have me. So Giovanni, I've been following some of your work. I find myself, to be honest, kind of getting convinced by it. I, I'm kind of-- I think I, I'd say I, I think it's a, a reasonable guideline or baseline of what's gonna happen, but I'd love to hear, you know, from you. so let's start with the beginning. Started the, you know, now listeners, you might have seen my earlier episodes with other, let's say, fans or promoters of the power law, but let's hear it from Giovanni. So

Let me share also my screen so we can go a little bit, deeper, in understand, understanding all these topics. So the idea is that, you know, many people Are trying to make sense of this phenomenon, right? The, the Bitcoin, price in particular, because, as much you want to be detached from that, that you know, it's something that, many people are looking all the time, right? When, because it's- It's a guide of where we are going and what is happening with, Bitcoin. I, I discovered Bitcoin quite early, I heard about, in fact, Bitcoin since 2010. and, I downloaded the wallet, I didn't do anything with it because it seemed a little bit at that time you can actually mine on your, laptop, you know? but it seemed a little bit too complicated, and I put it in the back burner, I thought it was interesting, I didn't take it I knew it was interesting, but, I never doubted Bitcoin, you know, I knew that it was going to go somewhere, but, I should have taken more seriously. But then, in 2012, I read an article, a kind of a newsletter where, people were, interested in technology develop-developments, in particular, you know, life extension, but also AI, and Bitcoin was mentioned, and this, you know, AI 12 years ago was Not as prominent as now, so it was like, you know, futuristic, you know. But, and Bitcoin was presented as one of these futuristic technologies, and in particular, one of these technologies that if you, You know, joined and if you invested in it, it could free you and make you actually, capable to be, to do things like Elon Musk, you know, to do like incredible project if you were interested in these, futuristic, ideas and maybe make them become real. And so I was, that kind of spoke my language, you know? And, I, it was, really the event of it, Orange Pilmi. And in the article, it was a chart, you know, in the chart, now this was two thousand And twelve, so you can imagine, you can imagine there was really little data. They had mostly, like a huge big bubble that happened in two thousand and ten, and a little bit more data after that, and the author was making the case was saying, "Listen, it's not a bubble." Because, usually bubble like the Vintar phenomenon, it's not a bubble. Yes, we did have a bubble, but it was a local one. And, you know, because at that time, it's al-almost nobody mentions the idea of tulips, right? Tulip, tulip, tulip. But that time is one of the things that they were mentioning all the time. These, they were making a parallel with, the phenomena of tulips that probably you are familiar, right? In the 1700, where and he was saying, "Well, it's not because, after a huge, big bubble like that, it crashes and it never recovers." But Bitcoin, Bitcoin did recover, we had a couple of years after that, and it's since, is growing exponentially. And exponential is something that is very familiar with, this technology development. I, you know, I was a fan of, I'm still, I am, of this, futurist called Ray Kurzweil. I don't You are aware of him, yeah. So this kind of idea of like

technology is gonna advance so much that we can live for very long periods of time and nanotechnology and AI and these kinds of things and robotics and that, yeah.

And he wrote this, two book. One is called The Singularity is Near, several years ago, and then now recently another one, The Singularity Is Near Rare. and they-- it's, these are thick books, like these pla- plenty of charts that try to predict the future, you know, where, his idea That there are very precise trends in human behavior, because that is one of the things that many people doubt, right? That, humans can be described by math, and, he said, "Look, you know, technology is, an artifact of humans, and it does follow a law. you know, everybody's familiar with Moore's Law, for exam- for example, I would say is that, the computational power of, chips, is, going up by a factor of two, Every, two years. But, he's able to find, patterns like that everywhere, everywhere, in particular when the knowledge becomes digitized, like for example, medical knowledge is becoming much more digitized nowadays and, it started to, became exponential in that fashion. And so I thought, oh, okay, Bitcoin follows this exponential pattern, you know, this person says so. So this is where my interest in- And trying to understand Bitcoin scientifically started like early on, you know, actually even before I bought my Bitcoin, first Bitcoin, I started to study charts and I downloaded the data, I started to model it. I wasn't convinced that it was exponential, and but, you know, I saw the regularity and I saw that Bitcoin was different from anything else, you know, like I started to compare. I had a, I have a almost now thirty years, Background in data analysis, you know, I am, my background is I have a PhD in astrophysics, so I started, I studied data in many different contexts. I studied in astrophysics, then at a certain point I pivoted and I went to neuroscience, I started to study the brain, and, I studied now financial systems. So I, I, I pick up All the things that I needed to know about the economy, ab-about finance, and I use the same tools that I was using to study stars and to study black holes, and I use it to study the brain, because it's basically the mathematics is very similar, in, in physics we call them universalities when we see similar patterns in many different fields, you know? And then, even when I applied the same tool, you know, to understand periodicities, to understand- patterns to financial systems, I started to see the same regularities. And one day, I was listening to this, video, I don't know how I ended up, but, I was, in Florida with my girlfriend and we were watching interesting videos, and I saw these videos about- It's called The Surprising Math of Cities and Corporations by this, physicist called Jeffrey West. He even wrote an entire book, on this topic called Scale. That is a, is a book that I recommend everybody to read because this book, is almost like a, like a Bitcoin standard. I think if you want to understand Bitcoin, you should read this book. It's a very beautiful book. and, in this lecture, he was talking about, cities and And he was saying our cities follow this mathematical pattern called power laws, and I will explain in a moment what, what power laws are. But, I was very surprised by that because I found these power laws, they are very common in physics, so I was super familiar with what a power law is, but, you know, I found them in astrophysics, in the brain, how the brain works, but I didn't know yet about human system, besides maybe the, some of the finance.

s-system that I was studying, but I didn't realize even cities were actually predictable in their behavior, like the GDP, the number of gas station, the number of library, how fast somebody walks in a city, the number of, terrorist attacks in a city, you know, the crime. All these things that people will think are completely random and unpredictable, were actually can be described by this power laws. And he added this almost poetic description Of a city, where he was saying, you know, the streets of a city, the communication system is almost like the arteries of the body, and, the, the, you know, the, telephone and cables, lines are more like the nervous system, and that. So he was describing everything, almost like a living city, an organism, and it was a very beautiful picture, but also- In science, we, have this im- imagination, but it's, funded on equations, right? On math. So it was showing the math supporting this. And almost immediately, I had this vision where Oh, he's talking about Bitcoin. That is also what Bitcoin is. And I went immediately after the, the video, and I download, you know, I had all the data ready, I started to download more on-chain data like, addresses and hash rate and all things, and I started to discover these power laws, this relationship, in particular, the first power law I found was price and addresses, and I made a post, I was very active on Facebook at the time, I had like a large group With thirty thousand people, you know, was not very active on X, and so this where my adventure, started in understanding the power law. Eventually, though, I was missing a, a key component that was How the, address is growing time, because I was under the impression, you know, again influenced by my reading on technologies and cetera, that it followed an S-curve, because everybody always mentioned like the S-curve of adoption, the S-curve of adoption, and most ninety-nine percent of the influencer that discuss these things on, on the X space, they claim it without ever showing a graph saying, "You see, it does follow an S-curve." It does the, the, I was doing the same thing, and I wasn't going anywhere. My model of, price versus, time weren't always not working. And the missing piece was-- Sorry, Giovanni,

can we just, just while we're on the topic of S-curve, I think it would be good for you to explain this also, because a lot of people say, "But Giovanni, the internet and email and things like this grew on an S-curve." What's your view there?

Actually no, because, let you see, many people claim these things without, and I don't mind, I didn't, instead of giving you like our overall picture of it, but we can still do it, but, I didn't this, talk so many times that people can find maybe we can do a deeper dive, right? And answer some of these questions. So the S-curve, when many people discuss, is this one, right? basically the idea is that, There is a distribution of, adoption. So you start, you know, this is the typical bell curve that everybody's familiar, right? It, it will be similar with height, right? Where you have, small people on the left, tall people on the right, and then the majority of people is in the center, right? And the height here represent, how many of these people find themselves in one of these boxes, right? In these, sections, with height This will be the average height. Of course, it will change from, population to population. If you're dealing with male people, you know, male, so female, you know, in this case, we are talking about adoption. So you can divide this adoption in innovators, early adopter, majority, late majority, laggards, right? And then if you add all the people that are joining in, right? and are adopting the technology, you are getting this famous S-curve. So- Basically, the S-curve is nothing else for the people that know a little bit of calculus, this will be the integral of this distribution, but simply is the sum. You are summing up, and you see it's growing, growing, growing because you have more and more and more people when you reach the center, while the people are starting to go down, there'll be less people, right? So it's not growing as fast. It's kind of here, in, in the same time, this is the peak of the growth of when it becomes faster,

and

then Then it kind of slows down and finally it saturates, right? Because, you don't have many more people to add. And this what, many of these influencers are waiting for, they are this mythical event,

right? Because we're just at the knee of the S-curve and this kind of, that's kind of part of the po- you know, the, the narrative, let's say.

And so time, you know, because, if this curve, this adoption curve is, much more narrower, you know, it's kind of like there is a A very fast, adoption when we reach, the middle, the S-curve looks almost vertical, right? And so they are saying, "Oh, it will happen so sudden, there'll be this, jump in the price, right?" Because then, if this is the adoption, the adoption is affected, is affecting the price, and they, and they never tell you how, but, You know, supposedly also the price goes up. And, my f- some of my first model I posted is, I don't know if I have it actually sh-uh, to my slides, but, when I, when I was working in the beginning, I solved this riddle that is, so here I'm showing all the major- Relationship that, eventually I discovered. The first one is actually the one in the middle. I discovered that all the way in two thousand thirteen, and I posted instead of writing papers that I should have wrote, wrote, right? I'm going, I'm actually in the process of writing a paper where I'm writing all this thing together, but, I was posting on Reddit mostly, because I, you know, I was, a professor, but also at that time I was actually a professor in the university, but also I'm very interested in teaching and reaching out to the community, right? So I understood that Bitcoin, Bitcoin was also a community, and I wanted to interact with other Bitcoiners. So I post instead of writing an academic article that nobody read, besides, you know, the specialist, I wanted to reach the community. I have done both, but I focus on reaching the community. And so the first relationship what describes, it describes the relationship between price and addresses. And you see, it's a power law. Yes, of course, there will be some variation. So let me say a little bit about power laws. Power laws, in the, in the physicists are always looking for regularities. So I think that it can be described by an algorithm, if po- you know, as a, as a second thing, if we don't find a formula, then we do, we create an algorithm, but if it is possible A formula will be ideal because a formula is really a simple equation that describe how one quantity relates to another. One of the simplest relationship that we find everywhere in nature, because a lot, a lot of natural phenomena are described by this type of relationship. It's a technical term, I didn't invent it. It's called a power law. law means a regularity, something that you observe over and over again. even the law of gravity is this regularity, right? Some regularity are stronger than others, but, in general, when you see this regularity, you call it, a law. And in this case, it's a power law. Why is a power law? Why is called power? Because you have a relationship of a type, and maybe I have a slide where I, I show it. of, of this type where, let me see, let me show you, we find, we write slide that I want to show you, like this. So a power law is something that looks like this, where you have Y, one quantity, and then you have another quantity X, and I can give you a couple of examples. And then, you know, there is a constant, this constant is not very important, it's like relating one quantity to another, even dimensionally, because, you know, you could have, like, for example, in Price and time, so you have to have something that relates the two, and then you have this quantity x that is a power, so you're taking The power, right? You're raising it to the power, like, for example, when you have a parabola, right? Y equals x squared, you're taking the square, you double, x, you get, four times y. You triple x, you get, nine times y. but this n Can mean any number, it doesn't have to be an integer, can be one point five, one point three, it can be negative, so if a one goes down, the other one goes up, it can be a fraction, you know, it can be different things. and it's a power because you can call it an exponent, you know, the technical term. In, in math and physics, we use this technical term, like, you know, in every field, you can call it an exponent or you can call it a power. and so this why it's called a power law. It's a relationship between two quantities that are related by a power. The power makes it very non-linear, that is what I just described. A small change in one quantity because of that power can create a big change in the other. Bigger the exponent, bigger the change, right? And with Bitcoin, it's a power law because we found out that there is a very nice, Mathematical equation we describe a, a large part, in fact, it turns out ninety-four percent of the behavior of Bitcoin can be described by this simple formula. I know it seems incredible, but it's what the math shows, and many people you interviewed some of them, right? I think you interviewed Sina and Seta, there is an entire group of people who now confirmed this result and verifies it's true, it's not just me.

ninety-four percent of the behavior of Bitcoin, which seems so complicated, can be described by this simple formula where A, this constant is ten to the minus seventeen, so it's a very, very, very small number, and I can tell you why so small. and time, that is the crucial thing. So it's a relationship between price, time, and a power that is a number that is very, very close to six. It's not exactly six, but close to six. So it, it's a power law. There are many of these power law in nature, I have a, an, these slides to illustrate, the, the relationship between, the distance of a planet, and how much from, from the sun, and how much, it takes for the planet to go around the sun, it's a power law. Now, in physics, we use this tool, it is a standard tool, again, it's not me coming up with this, it's what physicists use all the time, and you know, it's kind of a little bit funny because there are all Don't have a, a preparation, we didn't spend decades trying to study these things, and they think it's, you know, we are drawing a line by hand. No, it's, it's very difficult to find things that follow this line, in particular over many order of magnitude, right? So when you have something that changes, like with the planet, some of these orbits are, are, see, here I describe in terms of, AU, which is astronomical unit, that is the distance Distance of the Earth from the, Sun. So, you know, when you see a hundred astronomical units, it means the planet is a hundred times more distance, the, the Earth from the Sun, a fraction. So you go from a fraction of a, of an astronomical unit all the time to almost a hundred times, right? And these are the years. So when you have something that spans, many, many order of magnitude, so one, ten, hundred, thousand, right? Every time you go up by ten, that, that is what Order of magnitude means, taking the logs, it's the tool that we use. So we take the log of the x-axis, the log of the y-axis, and if you see a straight line, it's something that you can derive easily if you know a little bit of algebra, and anybody interested or should try to do that exercise, is if you see a straight line, it's a power law. And there are many of these straight line in a log and log graph that is where my contribution came. I know it seems trivial to say, "Oh, I took the log of time," but my question to the people that think it's trivial is, "Why nobody ever done it before two thousand and eighteen?" Because see, when I told you I got stuck I finally had a breakthrough when I decided to plot directly the price versus the log of time, and then I found out it's a, it's a power law. And now I had to go backwards and say, given that I found a radial power law between price and addresses, what that implies, right? And now I have all the sequence, so I can tell you exactly how it works. in fact, I can show you in a moment the graph of that, but if you want to, let me just try to

understand. Let me just sort of Try to explain it in, I guess, how I'm understanding it, right? The idea is that in nature, there are certain things that just follow a certain, you know, power law, like, like you're saying, right? So the, the distance of these planets from the sun, follows a certain law that it kind of, I guess, it sort of seems strange that they would kind of fall across this line in terms of how far away, but funnily enough, that, that's what they do. And then similarly, I think, in this book, Scale, He mentions a few examples, but one is around shipbuilding and another was around the, I think the calorie level that animals take in and like kind of their size as well, given kind of their size level and how many, calories they, you know, and their mass, and so then it kind of, again, a similar kind of idea, it sort of follows a power law and it's not just kind of like, it's not just A, a simple extrapolation, it's more like, a certain, scale, I think it's like a two-thirds kind of rule that, he mentions there, right? And it's kind of, it, it's kind of a fascinating thing. Every phenomenon we

have is on, DNA, so that is one of the things. So you, you summarize it very well. So for example, here we have this, very nice relationship between the mass of an animal and, how much calories they consume, right? In this case, we are describing Energy, right, Watts, it is, joules per second. So basically it's a unit, you can use calorie or you can use more like physics quantity like Watts. In fact, look at, for example, the human being is hundred Watts, right? That is like a bulb, but you know, we are, we consume as much energy as a bulb. It is really interesting. and look at this, right? Something that you will think is super complicated, like, the metabolism of an animal. It is one of the most complicated biological- Things. As you go to larger and larger animal, you notice a pattern. This is one of the things we, you know, as scientists and as physicists, we go crazy for, like As can-- it can't be that it's by chance, has to be that there is some kind of mechanism behind this behavior that needs to be understood. You see, these are scientists who will understand. He won't simply say, "Oh, okay, this is cool and it's interesting." He wants to understand it. What is going on here? I want to go deeper into the rabbit hole. I want to understand the mechanism. Maybe because if I understand it, maybe it's telling me something very important about the biology, the animals, how nature works. Works maybe something about evolution, all kind of different interesting things. And, and the, so you say about the planets, then there is, the-- but there are literally hundreds, hundreds of these, patterns, both in the physical world, in-- See that is the thing that I'm arguing with all the time with a lot of people that are not familiar with the science, with the literature. It's not just, Physical systems, and by the way, what is behind this? It's the law of gravity. So, it took hundred years, like when this was discu-discri-discovered by Kepler, and then he didn't know, he found the relationship. By the way, by measuring the slope of this relationship, in this case, is two over three for the planets. so you measure the slope and it's two over three, that n that we described before by the power. So Basically says the distance, of a planet from the sun, is related to how long it takes for the planet to go around the orbit, two, the, two to the three, the power of two over three, and that number needs to be understood. And for a long time, you know, everybody was shocked when this, this was a big deal when it was discovered, because for century and century, people were, were trying to understand how planet move. And Somebody came and said, "Listen, there is a very simple relationship." In the beginning, of course, we didn't believe it, and when more people verified, and everybody was shocked, and the question was, "Why? What is behind? What is going on?" Right? Then hundred years later, Newton came about, and he wrote a big, huge book there to show why, and it was all due to the law of gravity. That, by the way, is another power law. So you use a power law to, to describe another power law, but it was a more deeper power law It show that, you know, the attraction between the gravitational attraction between two bodies, w-went down with the square of the distance, and that could explain this behavior. and when people study these, it see, it's not the, it's not the same, but slope is actually different for different phenomena. It's almost like a certain different

power laws, and they have different, let's say, exponents, but the point here is that they are following a certain t- a kind of relationship. Yeah. Being called an exponent or a power law. so a,

a fi- a physicist look at this and say, what is similar, what is different? What is similar is this general behavior, right? It is, following basically this line in a log-log graph, and what is different is the exponent. So for example, for metabolism is three quarter, and, if you read the book, you know, he has an entire chapter to explain why is three quarter, and as, you know, just kind of a spoiler, has to do with, The fat that the body's a network and the type of distribution of vessels in the body to bring the food to all the different, part of the body, it's a fractal and, it's not, it's, it's a game between, the three-dimensional fat that, you know, the, the fact that we have a three-dimensional body, this where the three comes from, and the fat that is Almost like four-dimensional because, they, it's so intricate, you know, the, the circulatory system is so intricate that it almost goes to the fourth dimension in a sense. You know, it's a, if you understand fractal, etcetera, it's another rabbit hole. you, you understand? I think one,

one thing I think a lot of people want to know though, kind of if we bring it back to the Bitcoin aspect of it, as you said, it explains ninety-four percent, as you were saying, but then what about these kind of periods where Bitcoin Everyone knows goes through these big kind of bull market or bubble aspect and then it kind of drops down again. So in your view, can that aspect be modeled also, or, you know, where do you-- where is the science and where is the art here in terms of understanding the kind of- The bubble part or the bull part of the cycle.

Okay. And, and give me just one minute because I wanted to conclude a thought about this slide. So, you know, because one of the criticisms that people have is, okay, it works with planets, it works with, and by the way, these are some of the other, physical laws, look at the list, right? With all the different exponents, all these long list of different, physical phenomena where all power laws, there is a recurring joke, you know, there is a, I found one time a T-shirt which says, "I didn't create the T-shirt." I went to a physics conference, all what I got was a lousy power law, right? Because there are so many power laws all over the place. But the question is, okay, it works with, physical phenomena, it works maybe in biology, but for sure human beings cannot be described by something so simple. No, it's not true because if you look, like we already mentioned, fat, this where my journey started, in, in- In realizing the power law also works for human phenomena, there are, by the way, physics is moving in that direction. There are entire fields of physics called econophysics, sociophysics, where we use the method of physics to understand social and, finance, type of system. and here you see, for example, if you look at, I, I don't have to go in all the detail, people can read off scale and cetera, but that- Although I

think I would point out here, I think it's, maybe this is where maybe we Or something, but I would say from an Austrian perspective, you would say certain aspects aren't, you know, you can't divine an economic law just by looking at statistical relationships, I, I think. I think that's

Austrian economic then is wrong. Is wrong because, you know, they just, they are, it's philosophy and, just a bunch of words, and, science is based on data. The data shows it's not true because, you know, if you look at- So I think it's, it's

more like there are Things that you wouldn't be able to apodictically say a priori. And so I think that's, maybe it's, it's kind of like, it's making a different level of truth claim, I think. It would be like saying, let's say, what is the evidence? I mean, I would like to,

I would like to see, an Austrian economic book, but instead of saying a bunch of things, you know, because anybody, this is the difference between philosophy and science.

Yeah. Okay. Well, if you're actually interested, I would re-recommend, So in his view, like the way he would explain kind of Austrian methodology, is he saying that the way you do economics isn't the same as the way you do physics, right? It, it, that's kind of what he's trying to say, saying it's a different science. But see, I don't

agree with that because I am an econophysicist and I don't agree. Right. So I think that's

one

area where we disagree, but I think the way an Austrian would see it, yeah, I will. But, what there is to disagree, I would like Economic parameter, it follows a power law, and people did it for hundreds of cities, hundreds. So, listen, maybe there is something good in asset economic. When I'm writing myself a book and where I will have a chapter on asset economics, given that so many people like them, they like it because of a, a Bitcoin standard, but there is no evidence of that. There is no evidence, like people follow, Platonic philo-- you know, philosophy or many other philosophy, like one guy wakes up and says Say, "Oh, the universe is made of water." No, I think the universe is made of, of, fire, you know? And they debate forever, and it means nothing because they don't isn't, isn't made of neither of these things. It's much different, and you have to go deeper. The scientific method is what made everything possible for us, even us talking right now through the computer. Austrian economics what did it contribute? You know, I don't know. no, I

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with Austrian economic, but most economics is garbage, you know? And this is why I am an econophysicist. I want to bring the rigorous methods of physics and the, data-driven, That is my style, even in understanding Bitcoin. I don't care about people making, philosophy or say, "Oh, you know, if this thing happen, if this other thing happen," it's all a bunch of words to me. I want to see the data, what the data says, what we can learn from the data, can we use the data to make prediction, how good the predictions are. This is what worked, you know, for science, we revolutionize the world, we improve our life standards by doing exactly that. And I would- To do the same thing. Now, you know, if you have a,

a

interesting point of view, so the main disagreement

I would have with that then is that there are people who, let's say, take data or they kind of do this econo-econometric method and they ap- they take ideas and then apply them where they don't actually make sense. Right? They apply them where they are not valid. And so I think that's the main critique that, let's say, an Austrian would have of certain for-- forms of econometrics, right? But in terms of obviously the scientific aspects of, you know, the size of the boat or the calories of the animal or the, you know, the distance of the planets and the stars, that's a different thing.

We will have to see. And if you have a book, I definitely want to-- because I want to understand more, I want to go deeper, and I want to, you know, One day I will write, because besides a section in my book, I want to write maybe an entire book about what I think about external econ- economics in particular as applied to Bitcoin.

Yeah. It

could be book number two, given that so many people like it. my opinion right now, and I'm, I do have to admit, because as a scientist, I need to be always time transparent, I read a little bit, I start, you know, in particular, I'm very familiar with, Amos' work, I read the Bitcoin standard, Some of his economic books, et cetera. But I want to go deeper and I want-- because before talking about something, I want to become almost like an expert. For example, I am a very strong critic of S2F, and I had to become a world expert of S2F. I know S2F more than Plan B. So I want to know on a certain point of the economic so well that if I criticize it, I am an expert in it, and I am not. So, so far what I, what I listen, For example, Hamas on a certain point he will say, "Well, you know, it's not like a gas. It is like a gas." You, I can make many example and show you exactly like, there are many social and financial system that behave like gases. The only thing we can say probably, where maybe we find some, place where we agree, that the individual being At least at, at this point, it's very, very difficult to model. We are talking about large number of groups when they interact together and when they, in that case, they do be-be-be-beave like particles, very much like so. there are, you know, there is this entire field that I'm studying right now is called log-periodic power laws, that is, work from another physicist. He can detect days ahead, the a major correction, simply because it finds these oscillation in the market that are very similar to what you find when a material cracks or when earthquakes happen, and you can identify, I mean, you can see, I did it, I did it recently with the XRP live. I was, I told ten hours before, before a, a correction is going to happen in the next few days, it's going to happen now. It works. so there is- No doubt that b-people can be described like that. One day somebody challenge me and say, "Giovanni, okay, what about history? History for sure isn't a power law. It took me literally five minutes to find, for example, that the time in between wars is a power law. The number of casualty in a, in a war is a power law. I mean, there are all kinds of things like that. It's just that people think that we are so much free and they don't understand that there are regular- Yes, very well. This why you do have much more noise. Like if you go back to these graphs, right? You can see there is much, there is almost no noise at all. It's like crazy, so perfectly, regular with a planet. By the time you go to the animals and talking about physiology, there is much more randomness there, right? The dots don't follow perfectly that line. By the time you go to cities, you get much more fuzzy line, right? It's not as good as if it was planned. There is More noise, there is more indetermination. Yeah, and I think that's probably,

that is probably one point that I believe most, I believe most Austrians would say, yeah, I think that's the point that they would sort of hang their hat on and say, well, it didn't prove, you know, it wasn't exactly on. But I think it may be true that, it kind of generally is a guideline or a bench or a benchmark or a baseline for how to think about a certain thing. It may be true. So I, I think that's for me how you would

philosophically we can agree also, because I know where they are going, where they are saying, when they are, econo-economists, they want to use where, and in that case it's also bad econometrics, they don't use physics, you know, because they don't listen to physics, They use these very bad models to make policies, and then they want to impose these policies to people, and they don't realize how complex, the human, world is, et cetera. In that I can kind of agree because, the knowledge from these things, I think it can be still used, but then it should be more about, you know, facilitating, ne- for example, if there is a lesson, right? If there is a lesson that we derive from Bitcoin, is that in a sense you want to, you don't want to intervene, you want to let Bitcoin do the things it does, right? So it's like you want to understand it, you want to describe it, you want to study, maybe you can do things to- like for example, we can go in the bubbles, et cetera, to understand this periodicity, and you want to ride along, but I will never say let's use this knowledge to something, to something and intervene. If anything shows that if we have a system like this that is optimized to be as good as it is in, in terms of interaction between people, these network relationships, this scaling variant behavior, in a certain sense, is ideal for Or it's almost like a compromise between, the ideas that I have about the universe and actually the Austrian economics. In fact, I have actually somewhere here, a comment from Amos himself, and he said, "You know, Giovanni, maybe Bitcoin is the only place where, what you're describing will work, because it's so..." Perfect of a system where maybe it becomes like a, a metric of value and the only metric of value where this regularity are, you know, I have to find. But, you kind of agree with me, it was open to this compromise. And it's, it's a big deal for a, an Austrian economic person to agree on that, but, I'm open to that idea. You need more data, you need to show lo-longer term, but, is-it is possible that this is the case? You know, this is what he said, and I was very impressed by that because he, he gave an opportunity for an opening, you know, where we can compromise, because Bitcoin is so beautiful, you don't have to touch it, leave it as it is, you know? so maybe we can compromise. Okay. Yeah. So anyway, let's bring

it back to the actual, discussion. I think, you know, our disagreement about Austrian economics, we can put that to the side for now. Yeah, we can have another

discussion at another time. I came back,

And then we can have this discussion. but, right now I wanted to go back, you know, to the adoption thing and why we don't see S-curves, right? So this is where the S-curve. Now, how, what we will see, if we add an S-curve at the adoption, right? We, we are so lucky that we have, so much data about Bitcoin because, sometimes we are proxies, like for example, addresses, right? Addresses are the best we can do to, in, in terms of measuring How active is the network, right? Because the, basically the ideas that we are, reaching is that Bitcoin is a network, and if you want, I can give you some ideas about what network cards, what are the component of a network, I will, I will tell you in a second. But, this network, you know, if it was following an S curve of adoption, the addresses will look like an S. In, you will have to show it in, in a linear, graph. You know, it will look like this, it will look like an S. Now, in a, a graph where you're taking the log of the, addresses and it will be linear in time, it will look like a straight line. It will look like a straight line. And it doesn't look like a straight line. To make it look like a straight line You have to take the log of time and the log of the addresses, and then it does look like a straight line. You see?

So I guess in a way you would say statistically speaking, it's simply not an S-curve, right? If you just, you know, that's the answer. Right.

There is no evidence for it. Where do-- Unless again, you are wishful thinking, you are imagining. We have a data. This is, this is what I'm telling all the time to everybody. I had actually a meeting with Fidelity where they were, talking about this This curve said, "Can we have a meeting? Can they show you the data?" And we had this meeting, I said, "Look, this is the data, this address fits a power law, a beautiful power law. It is the, it's a, address is equal time to the cube." So it grows with the cube of time. This how adoption works in Bitcoin. And, and so it, it isn't this way. It's very counterintuitive. You know, you don't have A curve where you have innovators, early adopter, early majority. Yes, of course, there are people that join in early and then, but it will never, it doesn't curve like this. Basically, it's what is called scaling variant, that means it's going to look like itself. It's always looking fat because, you know, to go from here to there mathematically, you will do, you will take this curve and then you will defend, by taking what is called the, derivative. Of a, of a S-curve, and you will get this. If I take the derivative of power law, guess what? I get another power law. It's still a power law. The, how the distribution works is also a power law. So there is no, characteristic, event. There is no a place where you say this thing is going to go crazy, is going to do the same thing. That is a beautiful thing about power law. We have this property called scaling variance, which is the DNA of a power law. The most important, this why we are not like another model, we are creating a framework to understand Bitcoin under this idea that, these are what are called scaling variant phenomena. It is one of the biggest deal in physics, like we, we have entire book, you know, this, this topic called critical phenomena. It's basically similar to things like avalanches or sand piles or, when a system goes- From water to ice is an entire field of science, of these very, very interesting phenomena that are kind of on the edge, on the edge between being regular and irregular, chaotic and orderly. And Bitcoin is such a thing that is beautiful and fascinating, you know, for a scientist is such a, an incredible thing, but has also a lot of consequences if you want to really truly understand how Bitcoin works. So the idea is that, adoption is a power law It grows with the cube of time. And by the way, I was very puzzled by that and they say, "What is going on? Why a cube of-- Why the cube?" You know? And then I started to look, and it turns out in certain situations, usually, the spread of a virus is, like an exponential, but in certain condition, it follows a power law. And in fact, look at this, for example, eight and over is not a, a good idea. But think about- Memes, right? Memes are a kind of like a virus, right? Or, idea, like a beautiful idea, like, you know, when you spread, like a, you know, a, a good religion or some-something that changes people, right? It can be understood like a virus, right? You're spreading this new idea. Basically, this what Bitcoin is, is a ma-mind virus, right? We are infecting all the people with, with the orange peeling, right? So, and they do as, Hello. You see here, for example, don't know if you can see, I can make it bigger. You see where it's a power law because, you see this is how the, disease di-diffused, where it's a cube, exactly like a pow- a Bitcoin. It's not interesting. And I found it's not, you say, "Well, it's chance." No, I found many, many other phenomena with exactly diffused with the cube. Guess what? You were mentioning the Internet. This is one of these things that they say, oh, it's an, the internet is an escrow, and they always say, "Do not, trust, verify," right? That is the Bitcoin motto. I went, got the data, and guess what? It's a damn power law. Also the internet adoption, in fact, I can show you the graph for that, and it turns out it's almost three It, it grows with the cube too, like two point six or something like that. let me find the graph where I, I compare the two. They are almost, perfectly the same. Let me find it. so even the internet, for example Follow this, pattern. And so the idea is that, it be, it behaves like this, like a power law. just give me a second, I, I'm going to find the internet. Here it is. you see, this is the Bitcoin, a power law that is, so you are taking the, log-log, right? And the log, so it's a log-log plot, right? Bitcoin, Internet, look at this, parallel line that means similar slope, right? For Bitcoin, is a two point Eight almost three and for the internet, user is two point six, very similar ones. See, look at this, isn't it incredible? And then you have something else like a technology. Do you see how this looks like an S? This is phones, this is phones, cell phones, because cell phones isn't a network, right? sure people talk to each other, but no, there aren't no, in, in network, t- Facts that, fa-- you know, people are, watching an advertisement, po-- you know, some decide to buy the new, iPhone because it's fashionable and it looks like an S, you see? Oh, it looks like an S. And so this is cell phones, not a power law. Internet, a power law. Bitcoin, a power law. You see? And then, you know, I, I went deeper because this is one of the things that many people don't know. I'm working on these things twenty-four hours a day, even when I'm sleeping, and I found many, many different things, many different fascinating things. Like for example, I found this article where, they were studying different social networks, and they found out that, if you look at how social networks grow, they were, they expand. See, this is this paper That studied real life cases of network, this is a, it's, it's a Chinese paper, so it's mostly, China, Chinese, social network like WeChat, Weibo, this is like a lo-- what is called Los Alamos preprint, which is, you know, people posting online research papers. they include Enron because they had the data of the email exchanges, right? And you will think, "Wow, you know, Enron, it's..." It's a bad example. In fact, you see, Luca, you know, this is when people say, "What happens when if a power law breaks?" This is exactly what happens. You see how after Vanco, this thing collapsed like this. So it's a good example of when a power law doesn't work. But all these other social networks have both the nodes, because the idea of a network, right? You have a, these, centers. There could be neurons, in your brain, right? It's like a network, and then the what? That raise a network is that you have some units that process information or they do some actions if you are people, and then there are links that, connect all these activity centers, right? it can be people, it can be computers, it can be, neurons, it can be cells in our body, and then the other element is the links, right? There are these two things that are fundamental. And here in, in this graph, you see, we don't take the log of both sides because, You get that curve that we are familiar with Bitcoin, that rainbow curve, right? When, if you take the log of the y-axis and, and you take the-- it's linear in the x-axis. so it curves, right? You see how it curves like this. And but they are, if I did a, a log-log plot, it will look like a straight line. So this is a power law for the nodes, these are the links, power law links, et cetera. Yeah. This is the relationship between the nodes, the nodes and the links They reproduce. See here, I try to do the same thing with Bitcoin. These are the notes, these are the addresses. You see how it looks like this, exactly? And then this is the price, because the price Is related to the link where is this other network, property that says the value of a network is proportional to the number of links, right? So the price should be proportional to the links, and that is also a power law, you see? And this is the change. I got

a few reactions on that though. Yeah. Could it be that, I mean, there's other ideas like once you start measuring something, then people can start faking it or bluffing or spoofing. So as an example, could someone just start creating lots of addresses and, spend- And, you know, and kind of mess with metrics that way. But then I'm also reminded, in order to send to those addresses, you gotta pay fees. So I guess there's kind of a natural limit there. hash rate, obviously, that's harder to fake, like that's literally the point, like proof of work, it's hard to just kind of spoof that. So obviously- That is a power law too. It's a beautiful

power law too.

And so,

yeah, and, you know, and these things, you have also to understand it's order of magnitude that counts It's not a big deal. You will have to have literally thousand, and then how many people are going to do that, right? It will look maybe like, you see here, for example, you can see there are some points that are, you know, kind of like outliers, right? A little bit of, they go out of it, because, you know, these are also associated with the bubbles, and we can discuss the bubble in a second. So, and you will have an outlier, it will look like an outlier, somebody with- Did something stupid, but in general, the majority of people will follow the pattern, and you see how these patterns are basically the same. These ver-really, these relationships between, it's

gonna be like kind of, it's gonna get averaged out in the, in the noise or kind of it's gonna get averaged out once you look at the overall numbers anyway. Correct. but let's get to the bubbles discussion because I think that's gonna be interesting. I think one thing I've, I know you've been quite, critical of, let's say, the hopium dealers So can you explain your view there? Like, why is that hopey? M, what's the range of realistic here?

Yeah. So first of all, the general view of a power lawyer is that bubbles don't exist, and I sound silly, but, it's basically the idea is this, right? if I, there are We really think that the real power law is really what we call the support power law. This is this one, right? The, the one that you find first, because it's one of these things where you need to go deeper and deeper and deeper, right? In the beginning, you will try to fit everything, right? And say, "Oh, okay, there is a like a general trend that goes through." these, big bubbles, you know, it's a straight line, but, you know, and, and the, a statistic will tell you, in average, we seem to cancel because otherwise we wouldn't be able to get such a big, R square. R square is that number that tells you how good of a fit, your line is, and it's close to ninety-four, which means ninety-four percent. It can be like this if you have this oscillation, only if your oscillation basically cancel each other, and this graph makes it clear The, we leave, this, support line that, you can find the support line using different methods. You can look at sixty percent deviation from the line in between, right in the center. You can use, a method that is called the Ranzack, with, with basically you are, looking at, the data points that are closer to this, general behavior, that are basically the green dots, and everything else is almost like an outlier. So the bubbles are An outlier, but it's an outlier where they leave the, power law at the bottom. By the way, we think, it, it's something to do with the cost of production, this why we get the power law. when you go even deeper in the power-- in the rabbit hole, you find out that it's related to the cost of production, that is another discussion. So you leave a power law, and then for one year, it takes about one year to leave a power law And then you go back, another year, and so when we go up, it's exponential, then we go down again exponentially. And the two kind of cancel, right? It's almost like I could have moved along the power law, like the red line here, and not have a bubble at all. The fact that you

would have just-- Right. If you just kind of put your coins away in cold storage, you came back in three or four years, you kind of found out, oh, wait, I'm back on the power law. Anyway,

yeah. Yeah. Two years later, In one end, it's disappointing because you see your portfolio going crazy and then you go back, you know, to this more reasonable value. In the other, it gives you a sense of, safety. Many people contact me almost every day and tell me, "Giovanni, since, I learned about the power law, I feel much more conviction. I feel more, when there are bad days and we have big correction, I go and look at the power law and kind of, calm myself down, you know? I same thing, I do What is the real nature of this phenomenon? If it is only going up, we're really going up. One of the things that is amazing to look at, is when you actually- Average out, and you can do it, in the power law graph, it will look like a straight line, you know, for example, if you take, an average, this is another way of looking at this thing, you see how incredible it is. By the way, during COVID, we went there and we bounced off, you know, that is kind of a test, of this idea that, there is this, support line. But, I wanted to show you this graph where I'm averaging the price every over Window, and if you do that, and you go back to the linear graph, this how it looks like. It's, quite amazing. It's like how some people say,

"Yeah, I mean, while we're on this topic, I think some people almost think of the four-year moving average kind of like the-- That's kind of like, it rarely goes below that.

Yeah, so you can see that the power law is a very good model of the behavior over this four year moving average, right? Because basically the bubble are getting squeezed, or, you know, they get-- not perfectly canceled, but almost, but, and then, I mean, there is nothing to argue. It's, it's a damn good model of how Bitcoin behaved. And so the red line represents the, a summary, a simplification of Bitcoin behavior, and you can see it's pretty good, right? If I could zoom in in this area. Region, you will see follows, it follow from the beginning, and it, and, and basically is a J, right? It's not exponential because there are diminishing returns, and, and if you want, you can, we can discuss that in a second. But in general, the behavior is up, up, up, up, up, up, up, up, up, you know? In fact, some people say, "Well, it cannot go up forever." Well, I'm not interested in forever, I'm interested in what's up in the next twenty years, and I think there is Another episode and we can meet each other again and discuss where are we and say that, all right, I think what will happen is that we have hyper-creditization. Then there is no power law anymore. We, you know, it's another system where there's no anymore US dollar versus, Bitcoin, you know, we maybe don't even use the dollar anymore. So let's see what happened in twenty years. I think, let's focus in next ten, maybe twenty years at most. But let's bring it back to my

question as well, 'cause I'd love to hear

Example. So let's accept this idea, okay? Bitcoin is broadly following the power law, but every now and again, we get a one year crazy exponential bull market and then a bear cycle to bring us back down to the power law, let's say support line, for the sake of, you know, for this example. Why then is it that certain numbers are just unrealistic? Is it that you believe that would require going too far ahead of schedule per se? Like we're going, instead of going four or five years or ten years ahead of schedule, that's not realistic, but you think one or two Two years ahead of schedule per se is realistic or how do you, how would you explain that?

Yeah, so there are different ways of looking at it. One way is this, so this diagram, right? So what do I do here? I took the returns, so basically every dot you see here, so there are black dots and then there is the red line. Right. Are these like

monthly price or daily price or weekly or what? These are

yearly returns. So basically, is, given any day, you can look at What was your return over the last year? Right? So you go back and say, "I made, I made such and such, you know, today, if I look back one year from here, how much my-- and these are empirical value. Like it took, the imagine is January first, I take the price in January first, two thousand and seventeen, when you go back one year, January first, two thousand and sixteen, you take the ratio between these two, and that will give you the return rate." Return is meant in this case as a price two over price one. Clear enough?

Yeah.

Yeah? so every dot represents that, right? Every single day, I go back one year and I calculate what was the return. And you see here, right, for example, hundred means, you went up by a factor of hundred. And then, you know, you, you, your, portfolio went up hundred times, or your, the price went up, up, up hundred times. Of course, these large values are associated with the peaks. These were the peaks, obviously, because these were-- we get notice how the bottoms are much more flat. You know, they-- there is no really-- so what we notice about the peak, the peak go down. They go down in a very regular fashion, right? In fact, I can write an equation. This is a very precise equation. It turns out it's a basically... A kind of an exponential that goes down is actually an equation. It's one single equation that they can write that connects all these dots, all these peaks, and the bottom, it's basically almost like a flat line because this is what whenever we think we observe that, there, there is this support line in, in the bottom, if it's very, very regular, that we saw in the graph before. The blue line, what you see, is the The theoretical value associated with the power law. So in other words, if we were moving only along the power law, the return, the yearly return, will look like this. Right. So it's not just-- It is diminishing over

time. Yeah.

It's diminishing over time. It's not just that the peak are diminishing over time, the entire system goes down over time. And that is what differentiate a power law from an exponential. An exponential, your returns will be a flat line, will be Consistent like a constant

cago, right? Like it grows at whatever, seventy percent a year or whatever, but actually it's more like it's gonna taper down over time, which I mean, to me, is quite intuitive. I think diminishing returns is to be expected.

And the, its intuitivity, and listen, it was what defined Bitcoin, because in Bitcoin, in the beginning, Bitcoin to survive, if it grew like ten, fifteen percent, as, even some of the best stocks, nobody could-- maybe wasn't even interested in Bitcoin. What attracted Bitcoin was that, you were making like, you know, ten times a year or something like that, and people wanted to be part of this thing, can invest and bring, resources, etcetera, right? At the same time, you can't have something that grows ten times a year every single year, right? You see how the power law, once you start to think about the power law, you go under in, in this, rabbit hole that almost explains everything. Like even this thing that where it was important for Bitcoin to, it's almost, you know, like a, a little animal that needed to grow very, very fast, you know, like some of the orcs that come out of, of a mom and they run, right? Human beings aren't like that, right? It needed Came out and ran, you know, because otherwise the predators will have eaten live. So it needed to be strong and fast, etcetera. At the same time, imagine, you know, an animal that grows very, very fast because it needs to be, you know, defend itself from the predators, but at the same time, it grows every year ten times, right? Right. And at the same point, it won't have, it won't have food to eat, you know, it will die. And it's the same thing with Bitcoin, it needs to slow down. You Variable it is how much intelligence. See, this is where we agree with the str- Austrian economics. Don't touch this thing, it's great, you know, don't intervene, don't do anything, because it's so designed, it's so perfect, and it works with all the different human desire interactions, et cetera, et cetera. It found an intelligent way, right, through this interaction in the network, this how you get this natural system. It's all nobody's directing there, it's just the interactions that are working together and they- You know, there are, if you go too far in one direction, you, you are being pushed in this direction. If you go too much in the other direction, get pushed in this direction. In funds, kind of an optimal path, you know? So this is the optimal path, and you see how it's in the middle, it's in the middle of this oscillation. Now, the oscillations We are there, I think, because it's also part of human nature to go through these cycles, you know, this four-year cycle, there are a lot of people mentality,

people rush in, mentality, yeah, you know,

yeah, you see, you see, everything starts to be like a puzzle. When you have a puzzle where all the pieces come together, these are, you know, in science, you are in the right track, right? Like there is something into this. And so, and it's a story, but it's a story based on data, right? It's not just It allows, almost is like a, an escape valve, you know? It allows this, enthusiasm and this activity, okay, yeah, let's do this crazy thing. It's associated with the halving, it has nothing to do with the supply, it's more like a ritual, you know? It's almost like- A Bitcoin Christmas, right? And everybody gets excited, there is a lot of exuberance, and then it goes too far, and it needs to be corrected, and it goes down. You see? And this pattern, you can ignore it and say, "Well, you know, okay, it's happening this way, and it's so regular." But, you know, ETFs and the Saylor and strategic reserve and blah, blah, blah. No, because according to the power law, we have also an understanding of that. There are all these things, this is why we call it scaling variant Right? And let me give you this example, I was explaining the other day, and I think I even have a slide of that. Let's see if I have a slide, I have a slide for everything. And you see, look at this picture. this is how we think about these things, like, you know, this, this-- I took this picture from a lecture on, power laws. You see, power laws in space and time. This guy was giving this lecture, and he's giving an example, right? And this where I said, "Look So as an example, this is a, a simulation, right? It's a one of these cellular automata. I don't know if you have heard, like people create these little simple games in a computer to simulate this very complex system, but they have the same characteristics of things like, you know, for example, when we go here, you have an example, right? I'm going from, liquid to vapor or maybe solid to liquid and so on. Imagine ice, right? You're reaching this critical temp- Temperature is a TC, critical temperature, and as you come closer and closer to the temperature where water freezes, and you look inside the water, you will see all these little Clumps, you know, from the atomic level, you know, the molecular level, all the way to huge big chunks that you can see with your eyes of little-- it's probably something that you saw if you ever saw when water form, when ice forms, right? You will see small chunks, big chunks, if you could zoom in, you will see chunks at all the different levels, and this is what it represents, all these different chunks, and we call it scaling variant because it looks the same, it's self-similar. At all the levels, it's like kind of a fractal, right? It looks like a fractal. You know, fractal are, are like a tree, for example. You know, you look at a tree, like, modeling, right? Sometimes I can create a diorama by taking a small little branch, you put it on the, on the diorama, it looks like a tree because you don't know if you don't have a, a point of reference, if it branching, it's like the, a big tree, a small tree, you know, it's self

Like a tree, it has the same type of behavior. And same thing with this thing. So if, and guess what? If I organize the size of these, chunks by A many chunk with a given size, there are, guess what I get, if I create, I create a, a graph like that, guess what I get, what, you know what I'm, I'm, I'm trying, I'm trying to say, do, do you know what you get? A power law. So power law are associated with this type of, scaling variant behavior. That means you have, you are going to have few black rocks that are really big and they have a big effect, and then you are going to have, you know, banks and, smaller institution, which are, there are more of them, but, you know, fewer than individual. And then there is me and you, right? These are these little dots. And so- So I actually studied that, you know, look, I, I look at, I, I have this amazing graph that I want to show you where, I look at wallets of different sizes and I see, and try to understand the behavior between the growth of the addresses, and, the price, Splitting with different contributions, let me find the graph.

Right. And I'm, I'm actually curious as well. I mean, I'm sure you're familiar with like this kind of eighty-twenty Pareto sort of principle. Yeah. Where, as an example, people might, let's say there's a sales team, and maybe the top twenty percent of salesmen have eight-- drive eighty percent of the sales, right? It's kind of like a similar-- All

right. That, that is a power law. That is also power law. The Pareto law is a power law.

Okay. And so then, in a similar way, you know, a few large wallets might be responsible for a very large amount of Bitcoin per se.

Exactly. So you see this graph, what I did here, instead of, one, you know, taking all of them like I show you before, right, the relationship between addresses, how the price reacts to addresses and then the total behavior, right? this is what we got before. If you, if you look at the entire behaviors like this, right? So these are all the addresses. This is This is how the price reacts to the addresses, which is almost square, which is this thing called the McCall flow, basically says the value of a network is proportional to the number of links. so we are very close to something that looks like is a generalization of the McCall flow. And then when you combine these two things, you get the behavior of the price in time, right? Because you have time, this is growing time, this is the relationship between the two. Basically, what you do, you multiply the two exponents, you take three, you multiply by one And this where that five point six five, comes from, that, you know, that slope of a general power law, that where it comes from. If you do it in this way, multiply this two, or you fit the line, you get within one percent, you know, so it's impossible it is due by chance. This is due because these two interact with each other, right? And so now if you do it in that way that I just showed you, where now you take, you say, "Let me check, all the wallets with, Zero point one Bitcoin, the one with one Bitcoin, the one with five Bitcoin, the one with, with ten. I, I did it with many, many of them, I just representing the four, you know, because otherwise it becomes too clutter. But it's the same idea. All of them are power laws. The one with the whales, right? Let's call them whales, the one with large wallets grows lower. Why? Because there are fewer of them, right? So over time, you're going to have fewer of them, so it doesn't grow very fast. It grows almost linearly It's a slope one, and everybody grows almost with three, you know, this is everybody. and then you ask yourself, okay, given this growth, what is the effect of these guys on the price? And you see, the whales, a small little change in the whales create a big change in the price, right? It's a steeper slope. In fact, the effect is almost five, right? Huge, big. It makes sense. The whales, you know, they swim and create big, huge wa- waves, right? They have a big effect on the price, and this guy is much less. You see? Then when you combine all together, you take these and combine with that, you get this red line. These red lines are basically models of the price if you only take the whales, if you only take the dolphins, if you take the crabs, they're all on top of each other. Basically, it doesn't matter if you're small, big, etcetera, you're going to create the same effect. This already shows that, you know, doesn't matter if we have all these new players, there are just simply one more thing that is happening in this scaling variant behavior, you see? And so when you put all these things together, the fact that over time there, there is these, diminishing returns, the fact that, there is no reason why, even Dinna ve- adoption by state, because it's simply the next big chunk, or many of these chunk that are, that are state nation, few, right? You can count on, on your hands. Or in other words, I think

we could explain it like, to bring Bitcoin up at these high levels, it just simply requires so much more money that, you know, it just even to get to two hundred thousand or three hundred thousand would be a huge, huge amount more money. So I guess in that way- That's also kind of trying to explain why this idea that, okay, let's say we're at a hundred thousand today or a little bit under today, to go to like a million in the next year, but like the system is already so big, to get to that level and not just have to stay at that level would require so much more, capital coming in that it just wouldn't be a realistic- And in a sense, you can

think that, we needed these, big interventions from these, big actors because unless we had these big actors, we couldn't go Thousand, you know, we-- it's not something that retailers by themselves could have done it, 'cause we are talking about trillions and trillions, right? Think about it. In these fifteen years, we are here and we-- the market cap is trillion, and by to, to double, we will need to repeat the history of Bitcoin over the last fifteen years. That is Part of scaling variant things like, you see, imagine I am a tier three, I am a tier three, and I say, "How long is going to take?" okay, if I double my waiting time, I waited, I bought Bitcoin at the beginning, like three years have passed by, I want to wait other three years. So every time you double the high, the length of, the age of a system, you go up by two to the six, right? If we round the five something to six, you get two to the six is sixty-five. So you double the time you waited from three to six years, you're going- To have your portfolio going up by six, it is amazing. Well, now the system is sixteen, sixteen years, so you will have to wait sixteen years to get sixty-five. But it's still amazing because if we are waiting, you know, where do you find another investment where you wait fifteen years and you get sixty-five times your money? Almost nowhere, right? But before you had to wait three years or, you know, two years or whatever, five years. A, a, and now you have to wait sixteen, because this how it goes. It goes with the age of a system. This how these diminishing returns work. So you can see it takes longer and longer time to go up and reach these high levels. But and it's okay because you see, we need the infrastructure, we need the security, hash rate, hash rate, remember, goes with the price square. So if the price explodes, imagine hash rate that isn't The infrastructure that are now in miners to sustain

the mining machines, yeah, mining machines,

the, the, you know, and there is the laws also, we need the laws, you know, to take, so actually it's a blessing that the system is slowing down. If you get out a little bit from your selfish desire of became millionaire the day after tomorrow, and you're caring about Bitcoin as idea and as a re- Evolutionary thing for the world, then you say, okay, you know, I'm going to have a little bit, see, this comes from Austrian economics, right? The preference time. That, that is a beautiful idea. That, if there is one thing I love from, from, you know, Austrian economics is that concept of time preference,

time

preference is beautiful. Bitcoin teaches us basically the power law, it's time preference incarnated, is exactly that, is telling us we, Patient, and you will be rewarded, you know. Don't worry, you know, what is fifteen years? Nothing. I mean, it's nothing for me, but I am much older than most of the young people. For a young person, he will, you know, go and do other thing, to enjoy life, and, you know, come back, and you will be much more wealthy than you are now. Continue to do DCA and so on, and, you will be rewarded. There is no reason, because if, let's say, if you read that book scale, right Corporation, the corporations grow as exponential, and if I studied hundreds and hundreds and hundreds of, corporations, and you can see the average corporation dies within, you know, many corporation die very quickly. The one that survive a little bit, the initial phase, they last maybe fifteen, twenty years. Almost nowhere you can find a corporation that lasted more than hundred years. e jokes that he says, "The Vatican is a..." That's a joke, right? So I guess the point

here, you're making here, is that cities are growing more like a power law, they're more sustainable, whereas a company can grow more like an exponential, but the downside is it can, it can crash or it can die. It can crash, it can die, they don't have

resources, they get a little bit, staff, right? They, they don't innovate anymore, they get really bureaucratic, you know, they are too large to change. While the power law, this is, it's a favorite For cities, but also there is this beautiful article, that I found where, we discover that, tooth, and nails, and horns, and horns, they all grow as power laws, because it's basically nature way of saying, look, I'm going to grow, but I'm going-- as I grow, I'm going to take my time to go to the next step. I'm going to take my time. I'm going-- it's basically the power laws, this proportionality between the growth of one quantity, in this case, price for Bitcoin, and In time, is a proportionality in scale. So if I go by a factor of ten up in price, I'm going to take a factor of ten in time. You know, a factor of hundred, a factor of hundred in time. So this means slower, still pretty fast, because you saw that J varies crazy, right? Time to the six is a very high, high value for time, but I'm not going to do it as an exponential, I'm going to do it as a power law. It's the best of both worlds, you know, because we're- We are still talking about forty percent a year and now just following the power law, and, you know, we are going down, it will take about twenty years to go down to twenty-five percent or something like that. So they're going to beat the stock market for the next twenty years, which is amazing,

you know. And as I'm understanding on the, you know, from what I've seen of the curves and the charts and things. We're here today, December 2024, but loosely speaking, roughly speaking, in let's say ten years-ish, Bitcoin will be over one million based on the power law, and in twenty years' time, it'll be over ten million dollars. That's kind of loose- Yeah, it's very similar

to what, Sailor says. I don't know if he actually studied the power law, maybe arrived to other, through other consideration, and we kind of agree. It's kind of interesting, that is thirteen million, right? He said thirteen millions in about

twenty

Yeah, exactly. So tw- twenty years from now, same thing with the power law, about, ten million in twenty years from now. It is incredible, right?

Yeah. This show brought to you by Mempool dot space, the world's leading Bitcoin visualizer, and now they've got an accelerator program. So if you have a transaction that you sent at a fee that was too low to get confirmed, now you can fix this at with the Mempool accelerator. The way it works, you can go and search your transaction, scroll down, click accelerator, and you don't need an With Lightning, and then it'll show you it's now in the process of being accelerated, and then after a few minutes, it's confirmed. And so this is a great way to help you out if you are stuck, and this can happen where maybe your wallet doesn't have RBF or CPFP, or it might help you in situations where it's impractical to go and re-sign, so for example, multi-sig with keys in different locations. And thirdly, even in some Lightning scenarios, perhaps a forced close, you might not be able to use RBF, and so in this case, So keep it in mind, and you can find out more over at mempool dot space slash accelerator. Okay. And then I guess for listeners who, who really wanna know, your thoughts on what you think is a realistic, like, let's say the same pattern follows out like we've seen, you know, in cycles past, gone past? Are you anticipating, like, where do you think, let's say, a top would be at the end of next year, and then let's say if we have a bear cycle, where do you kind of think a likely or realistic bottom would be, let's say, a year after that?

Yeah, so, you can do it in a couple of ways. So if you do it, for example- Considering this decay of the tops, because it's a kind of it follows like a mathematical pattern, so if you take at face value, you say, "Okay, I don't understand it, but even the top seems to decay in a predictive fashion." Where can I project this to the next bubble, right? You say, "Maybe, maybe it's something real, Vitta." See, this is where I say all the time is the weakest part of the model, so one should take it with a grain of salt, right? This how science works. When we are very strong, like the power load, you know, so much data, so much confirmation, thousands of points that tell you, "Look, this is a very strong analysis." When it's weak, I'm telling you too, because we have only unfortunately few oscillation, right? So Statistics are a little bit more weak, but if you take it as a, you know, at face value, then we are getting about two hundred thousand. So we go to two hundred thousand is going to happen in quarter twenty-five, and then we should continue to go down because until I see evidence that the cycles aren't real, I'm going with what I'm seeing. I see cycles, so I'm going to say they are going to exist in the future. And then we go down f-for one year and we are going to reach seventy K. So we go to two hundred and then down to seventy K, and it will take one year. So by twenty-six, by a quarter twenty-six 26, we go to

70k. Something like that, right? And so then, in your mind, what's kind of the realistic range of how much higher than that could it go? Without breaking a power law per se.

But it's, so remember what the power law says. The power law really cares, beside this decay, right, that we say, is almost like an additional analysis, it isn't really related to the power law. At least we don't know if it is related to the power law.

I say it's a,

it's a regularity that we see. In theory, if you don't take, you know, if you don't, if you say, okay, let's, let's, Free ourselves of this limitation, of this decay. in theory, I could have the power law going to infinity and come back to seventy K, and we'll not violate it, right? if he does it in the timeframe, because one also, as to be honest, one can say, "Well, you know, if he co-continue to go exponential for the next five years, and then it comes back the next five years, it's still a power law." I will be the first one to say no, you know, we are in a different regime. It will not be fair Science works, yeah, to be honest, right? So in my theory right now, I, I will be very surprised if we don't go down, you know, from the peak and then we reach the bottom. If we violate this, exponential decay, it will be one of the things that is, not happening. But then, let's say we go to three hundred and then we go down to seventy, I will say, okay, let's forget about this. Peaks going down, that was a fluke, but the power law still works. So if we continue after one year and we go up Again, and you start-- and we continue to go exponential for another year, then, you know, we will have to say, "Well, we aren't doing what we were doing before, for sure." You know, we aren't following this oscillation, so, you know, it's not-- it doesn't look like we are in a power law anymore. So this is where I will say, the, the power law is violated, right? We are, is-- and this, look. It's for sure an historical thing, right? You can't deny this. I mean, any scientist, not just by look, but also analysis, et cetera, has been part of the history of Bitcoin. And, you know, if one is interested besides making money also in understanding the system from an academic point of view, from a scientific point of view, it's a contribution because we found out all this regularity. It also allows us, to have a reference where if anything goes different, then we can compare before and after. That is also when models are useful, when things aren't going as you expected, right? Because now you can compare what you did before with what is doing next. So I won't be the first one to say, "Listen, you know, something is different this time." Like for example, there is one pattern that I'm warning everybody that is, is different because everything else looks ex- Exactly like the previous cycles, almost like a, a copycat of the previous cycles. Now, there is one thing that, if you want, we can spend one minute to discuss it, that is different from everything else, that is liquidity. so I did, I have made this model that is not Based on the power law is simply what I look at in terms of, relationship between global liquidity and, the price of Bitcoin. again, I'm looking at the graph at, I can show you, otherwise I can summarize it for, for you. But,

so I started liquidity like, different banks and different, M2s and so on. And, and it looks different this time. So this is the graph I wanted to show you. so, and this isn't an updated, picture because this is basically a purple line. It's, I, I didn't, I took up All these are parameters like M2 of different countries, different banks, and I added them together and then I try to find some kind of simple relationship between price and this quantity. There isn't such a simple relationship, there isn't, for example, a power law or an exponential, it's much more complicated. But the purple line is supposed to represent this relationship. It's basically, you can think of it almost like the fair value of, Bitcoin if it was on Only based on liquidity. And the white line is the price. So in all the previous cycles, what we always saw was that there was a, a lot of liquidity. Basically, the purple line was above the white line Just before, you see like here for example, you see we had all these, and when, when the tap ends, when the purple line is above the white line, I color it green. It means we have a lot of liquidity available. Then when we come close to the peak of the bubble, they switch, you know, like the white goes above the purple, that is kind almost like a definition of what a bubble is, right? You have a, you don't have fundamentals to support this foam, it's all driven by craziness, right? Like that is tulips, that component is tulip, and then the price corrects and we go back to where the, the white line is above the purple. This time is different And for some time, this where, this graph needs an update. it's a trading view, I make all these trading view indicators that, by the way, people can have access to if they like, they, come to my X and, I'll let you know how to get these indicators, is, you know, I have like a Discord group. But, basically, for some time we were seeing this where there was a price was going down, was going down, the liquidity was going up, so I was hoping there was some kind of crossing here, right? This would I would say, okay, we will need, we will have this crossing and we will get something similar to what we got before. Well, this is different because what happened, instead of coming together, the price went up, liquidity actually Went down. If we, if we were looking at an updated picture of this, it would look like we did exactly the opposite. We went in two different direction, and this never happened before in all the different, bull run. And I don't know how to interpret this. You know, it could be that we don't need liquidity anymore and only ETFs

and the- I guess this comes back to, you know, it comes back to, again, human action and choice, and these elements of it could be different, right? but, I am also- Curious your view because as we've spoken about, diminishing returns is, you know, to be expected, that's the intuitive outcome, contrary to what, let's say, the opium dealers are talking about, but Should we also anticipate diminishing volatility and, let's say, should the bear market cycles be less harsh, right? Like, let's say historically it was very normal to have eighty percent drawdowns. Would you expect that going forward, you know, it's diminishing returns, but also diminishing bear market drawdown percentages or not?

So as you can see from the graph that I showed you before, right, the bottom is always consistent Always consistent, but, the top is going down. So of course the correction if a top is going down. And by the way, this is my project, right? If you do it with this method using returns, you get something close to the value we talked earlier before. In this case, it's more like two seventy, two fifty, so basically here this red line will go there. So when we go down, there is much less correction, right? Because we didn't go that far away. so the correction will be smaller, but we always go back to the same place. So we, I'm still expecting to go, you know, from, seven from two hundred, we can even calculate it, right? What is, so if I do seventy over two hundred, You know, that is, point,

point three five. So

what's

that? Sixty-five percent

drawdown? Sixty-five percent drawdown.

Yeah.

Exactly. so I'm expecting a sixty-five percent drawdown, but was smaller than the eighty simply because we go to the same place here. So crazy

high, right? But if we theoretically did go to three hundred, you still would anticipate going down to seventy?

I think so, mostly because I think this line here, this support line, is almost like an attractor. It's basically, you see how regular it is here? Look at this. Now, these are Monte Carlo simulations. You know, I did this Monte Carlo simulation where I, I create the history of Bitcoin, like millions of history of Bitcoin based on the stats, and I let them run. You know, this is another thing. I did a lot, lot of stuff. People don't realize how much work I did. In this case, what I do, I take all the statistics from the Simulations, right? Over and over and over again, millions of them. This is, this what this gray line is, and basically, you know, it's like you're running, you're throwing the dice many, many times and you're recreating the history. And this is what I'm expecting here, right? And it's going down like that. There is some fuzziness, so we could be a little bit higher, a little bit lower, but it's still around that region, right? Simply because It's, like I told you before, it has to do with the, cost of production, so we correct, we correct and, and I- You know, thinking in these terms of scales and the scaling variants, I think actually the big actor could simply actually accelerate this thing, you know? It, it doesn't mean that people have the wrong ideas, they think that, they will be the one stopping. It's possible they create a chain reaction where, actually- Yeah, we do correct and, and pretty fast, and this correction have been very regular all the time, and we go the same place. So this is, this is my understanding right now, right? But as a scientist, you're always open to update your understanding, the regime could change,

something could be different, I mean, it always is possible. So, I, I guess it's not, to just sort of say, "Oh, I'm just following this chart, no matter what." Yeah, things could change, right?

Yeah, the way, the way to understand this is if everything continues in the same way, under the same stats, under the same mechanism, then this is what we expect. If something changes, then we go back and say, "Okay, what happened, right?" Let's try to understand Gain knowledge, you know, from doing that.

And this is

how scientists do things, you know, we know, and everything we do when we under-- trying to understand, you know, the universe, this is exactly how we do it.

Okay, well, I guess one other area that's maybe a little more controversial, I know you might have spoken a little bit about this, is, the aspect of trading. Now, I think, I'll preface this by saying I think most people who try to trade will end up losing because maybe they don't have the emotional or psychological makeup to sort of do it correctly. In practice, a lot of people end up buying high, selling low, because that's kind of historically when people are new, they don't really understand. But, I certainly understand that there might be people who I'm curious your view, how do you think about that component of it?

So I lived all the three bubbles, okay, all of them, experienced all of them, and it was devastating when I was, you know, today I was analyzing the market, I was making a video and I told the stories, right? Every bubble, I can close my eyes And I can remember exactly where I was, how I felt, all the emotion associated with it, and it was exhilarating. You know, imagine some of this crazy bubble, right? If you think our last bubble was exciting, imagine the one in the beginning, you know, this, this crazy one. Look at this, we were almost- Yeah, yeah, twenty- I was around twenty thirteen

as well, so I felt that, I felt the double top as well, sir.

Yeah. And, and then we crashed down, right? And that time actually was scary because we didn Of course, we had this first bubble, we thought, "Oh, okay, we, we, that was some kind of anomaly, we are going up, we are now going to have another bubble." And then we had this other thing, right? What is this? We were still trying to make sense of this, and then by the time we had the second bubble, peo- some people started to say, "Oh, this is going to repeat exactly like before, exactly like before," you know, it's going to be... And at the same time, it was some debate. At that time in 2017, people were talking about institutions. We were banks, we were, some large funds that were starting to invest in Bitcoin. Wall Street, was interested. We were investors, you know? this idea that, institutions, join the Bitcoin network isn't new. We were still talking about that. And I still remember being under the shower and some little voice was telling me, "Maybe..." Maybe you should sell half of it, you know, why not? It's a life-changing money, you know, sell half of it, let's see what happen. If it goes down, we'll buy at the bottom, you know, and, and, re-let's rebalance our portfolio. And then I had this other voice that was saying, "No, no, no, no, no, it's different this time, it's different this time, it's different this time." And then it was no different, right? And it was no different First of all, it's not very likely it's not going to be different. And second, today we have so many tools, right? If you-- So it's an entire range. It could be from Like for example, if you are doing this year, like even me, right? Every month I buy a little bit of Bitcoin, about every month, every month, every week or whatever it is, and I do it automatic. Well, when we are coming close to these tops And we should be able to tell where we are in terms of timing, in terms of deviation, all these different tools that we have. Maybe we should buy less, you know, maybe we'd go and start to put some of this money aside because you still want to do DCA, you don't touch it, you keep it in USDT, maybe in your wallet, you know, in a, offline wallet, then as we, as things cool down You buy more Bitcoin. E-e, you know, I know that some people think one Bitcoin is one Bitcoin, at the same time, one Bitcoin that is two, three thousand dollars isn't one Bitcoin that is seventy thousand dollars. And I know it's not US-- People will say, "Oh, but you are fixated with USD, you are thinking fiat." No, I want more Bitcoin. So if I can use some of it to hundred thousand, you know, because it's Bitcoin plus FOMO, one way of thinking that you have a Bitcoin plus a bunch of- To formo, I want to sell the formo so I can buy some Bitcoin. So do it in a, in a way that makes sense to you, right? Make a plan and see how you feel. intellectually, but also emotionally, and say, "You know what, that crazy Giovanni, maybe ten percent. Okay, I'm going to do it with ten percent. I'm not going to sell more than ten percent. I'm going to do it only with five percent." Or maybe, I'm going to, to what you say, I ca- we come close to that region, I'm going to put aside a bunch of, dollars and I'm going to buy when it goes down, right? Maybe this line or whatever, you know, you use some indicator, use some reference, when it goes down, make a plan ahead of time. There are options, you can buy a very out-of-money option with IBM or maybe, MicroStrategy that is linked to Bitcoin price, right? Buy something that is very cheap Cheap insurance almost, right? By, out of a, price option, you know, that is not going to cost more than much, but if there is a big, huge correction, you will make a lot of money with that option, so it compensate a little bit of your loss of value of your Bitcoin, and now you can use that to buy more Bitcoin. So it's part of what Bitcoin is that we have this bubble. We are blessed that we have a very general steady pattern up. But also we have a lot of volatility through this bubble, so why not to do something with it, right? And just it's up to you, you have to decide what is your style, what is your level of knowledge, your level of support, make a plan, decide what you're going to do. In my case, I will do a combination of these things, I will do all of them, you know, at different level, because I, I want to be prepared, I want to be-- This time I'm not going to You know, think when we go back to the bottom, I should have done this, I should have done this order. I will make a bunch of decision, I will stick to my decision, and I will be coherent with that. There is nothing wrong with that, right? Nothing, I don't think there is anything wrong.

Yeah, I think it's fair enough for people to think about it. I'd just say, be very, judicious about your planning, for listeners out there, you know, don't do anything crazy, never sell all your Bitcoin, you know? but, certainly, I think it's fair that, you know, people who wanna think about taking a small percent and maybe that's your fiat buffer for the next bear market, right? As an example, or maybe it's part of how you think about, you've got some income, you're Things are towards the bottom. also, got to think about taxes and fees, right? So these are other elements that people will have to consider and make sure, okay, after these things, am I still net up in Bitcoin terms? Okay, then, okay, maybe that's something you have to, you have to make sure you also think about. But, yeah, I think that's, you know, we've, we've gone for a bit over, but, I think, I think it's been an interesting discussion, a lot of interesting insights there around You know, power law, scale invari- scale invariance, diminishing returns, but also what does that mean? Is it a more consistent, you know, thing that can survive longer? certainly very interesting stuff. So listeners, check out Giovanni's work. I'll put the links in the show notes to the x and the website is, bitperseidin dot com and the YouTube channel is there as well. I'll put the link for that also. It's called, Quantonomy. Okay, so Giovanni, thanks very much for joining me today. My pleasure

Good questions and, to be patient with me and listen all this time. Thank you for the audience too.