{ "episodeId": "SLP732", "speakers": { "stephan": { "name": "Stephan Livera", "role": "host", "tag": "STEPHAN" }, "giovanni": { "name": "Giovanni", "role": "guest", "tag": "GIOVANNI" } }, "segments": [ { "speaker": "stephan", "time": "00:00", "start": 0.18, "text": "We talk about falsify because I want to people to accept this idea that we Bitcoin has a very structured growth over the long period of time. And I want to remind, when we are talking about long term, we are talking about years, right? So we're not talking about changes in the price on the scale of months or days. That is not what the power law is about. It's about this very long term trajectory. And it's important because, you know, we don't know, right? So if I tell you Bitcoin is- is going to be one million dollars in eight years is very different from somebody telling you Bitcoin is going to be a million dollars in two years." }, { "speaker": "giovanni", "time": "00:39", "start": 38.53, "text": "Hi everyone, and welcome back to Stephan Livera podcast. Rejoining me on the show today is Giovanni Santostasi. As, many of you already know, we spoke earlier on the podcast, but he is the, let's say, the founder or the creator of Bitcoin Power Law Analysis, and he's back to present and talk to us a little bit about his new book that's gonna be coming out. It's called The Physics of Bitcoin. The founder of the Scientific Bitcoin Institute and I, you know, it, it, for me, I find this stuff quite interesting. I wouldn't call myself a power law analyst, but I am, you know, I'm a fan. I've been sharing and, trying to talk about it also because I think it's an interesting framework for understanding different aspects of Bitcoin, whether it's the adoption, the price, the hash rate, and these different explanatory factors of Bitcoin. So, yeah, so welcome back to the show, Giovanni." }, { "speaker": "stephan", "time": "01:27", "start": 87.4, "text": "So much, yeah, it's my" }, { "speaker": "giovanni", "time": "01:29", "start": 88.76, "text": "pleasure. So, yeah, let's talk a little bit about, you know, why you wanted to write this book. By the way, it's," }, { "speaker": "stephan", "time": "01:35", "start": 95.14, "text": "it's fa- it's funny because, I, I'm doing a lot of AI, I'm using a lot of, you know, it's an incredible tool, and I was making a plan of how, you know, to let know people about, the book and explaining the idea. And one of the things he suggested is you should go to Stephan Livera podcast." }, { "speaker": "giovanni", "time": "01:57", "start": 116.58, "text": "So I'm in the AI somehow. The AI is telling people to find me. Yeah, like one of the top" }, { "speaker": "stephan", "time": "02:01", "start": 121.18, "text": "podcasts where I should go. So you will, I found it. Well, there you go. I think it's, it's" }, { "speaker": "giovanni", "time": "02:05", "start": 124.68, "text": "probably because I do, I do often interview Bitcoin authors, and so yes, yes. It probably, that's why it comes up in the AIs and whatever. So, yeah. But, yeah, tell us about why you wanted to write this book instead of, you know, just doing online podcasts and articles." }, { "speaker": "stephan", "time": "02:20", "start": 140.47, "text": "Yeah, so the book is actually kind of, is going to be almost like a reference book, you know, because it's, self-contained. it has, it's supposed to even to be a book that, maybe introduces Bitcoin to people who've never heard about it. So there is, an introductory section where, we cover the basics, you know, it doesn't go too much into technical details or, or to use Bitcoin, or to get, well, because there are plenty of books like that, right? and but I do mention The references, there are several appendix, appendixes that say, okay, read this, read that, you know, to get, this other information. But it's trying to make the big case that is what the power law is all about from the beginning, where Bitcoin looks more like a force of nature, right? It's, similar more to this other process. Basically, there are several important, assumptions, and I have mentioned these assumptions and the- His point of views in my post online, in my article on Medium, but I think it, the time came to put it all together and make a coherent story that somebody that never heard about Bitcoin and he thinks it is random, that it goes up and down and it doesn't have, has no value, reads these things and gets transformed and say, \"Wow, you know, hopefully maybe this became so one of the most powerful orange peeling mix.\" Mechanisms, because if I understand, Bitcoin isn't random, it's following a very precise pattern. This pattern is the pattern that nature prepares in growing different structures, tooth and nails, and at some point I mentioned this article that I, I mentioned before in my tweets about finding it in a book that says, \"Look, you know, nature likes the power law for all the structures, it's not just biological structures, but the universe, like galaxies, planets.\" And things like the language, the innovative activity that hu- humans do, cities, you know, cities are one of the s- most important inventions of humankind, you know, the entire civilization, the word civilization itself comes from civitas, it means city in Latin, you know, so, cities and civilizations are one to one. So all the things that are most fundamental in human life are coming from cities. And they follow power laws, they grow as power laws. So once you put Bitcoin in this context, there is this clear picture of what Bitcoin is, right? And then we can discuss this in more details, but, one of the biggest criticism of Bitcoin is, oh, it has no value. And there is an entire section, entire chapter of a book that takes all this information and tries to build almost a mathematical definition of value, you know, why Bitcoin is valuable. In fact, probably it will become the most valuable invention of humankind or system, whatever you want to call it, and it, and is connected to this power law theory, you know, all the consequences from the power law theory. So this is why I wanted to write the book, I want to reach a lot of people, I want people to use it, maybe to orange peel other people, I want to address the skeptics, you know, because there are a lot of skeptics, maybe we can read it, in a book format, we see the pictures, they underst- And, the concept that are linked to it, because I also build all these concept, the f-foundations that are necessary, we talk about, Self-organized systems, we talk a-about network, network theory, we talk about, power laws in general. So, yeah, it is, it is, there are many reasons why I wanted to write this book." }, { "speaker": "giovanni", "time": "06:15", "start": 374.69, "text": "Now, like I said, I'm with you, I, I'm a fan of the power law, but let's say a skeptic is looking at this and thinking, \"Well, are you guys just like fitting data to a curve here? Is it just like some kind of weird overfitting thing? And in a few years' time, these guys will just kinda come out with a new model because the old one broke and so on, that it's, you know, it's just a model.\" Can you explain why there's something deeper here?" }, { "speaker": "stephan", "time": "06:40", "start": 399.7, "text": "Right. Well So when, when I discovered power law, you know, it was doing this transformation that I discuss in the book by taking the log of the price and the log of the time, you can see the behavior by your eye. You don't even need to draw a line. You can see that something weird happens to the price of Bitcoin. It becomes kind of like a line, right? That immediately for somebody that is trained to look at these phenomena It immediately clear what you're looking at. You're looking at a process that it's proportional in terms of a scale, the scale of price and the scale of time, right? that is a deep, deep insight. Then you can use mathematical tools like regression to draw a line, because the line will give you the slope of the curve, so it kind of tells you the proportionality relationship between the scale of price and the scale of time. You can do all kind of tests, you can take out of it data and project it in the future, you could say, \"Well, what if I did this?\" You know, the history of Bitcoin is almost seventeen years ago, what if I did it eight years ago, will I have been able to see the power law? Remember, I actually discovered this in two thousand eighteen. So the power law at a minimum has been predictive of a general trajectory since two thousand 2018. And in fact, I saw, power laws, not the one in price and time in Bitcoin since 2012, the one between price and addresses, for example, that was my first power law, and I discovered that in 2012, you know? So this power law have been very consistent and beyond, and, you know, and today now There are several, several, analysts that are looking at this, but we go beyond being just analysts, we are people with, mathematics, physics, engineering background, and we did all sorts of stability tests to show that actually the power law in time becomes stronger and stronger, becomes more stable. And not just that, for example, some of my latest results was to look at the dynamics. So if you're looking at Bitcoin chain Changes in time, you can reveal the power law. So it's beyond just fitting a regression, you can look in at the changes in time and then study these changes and show that mathematically these changes are consistent with this power law behavior, this scaling variable behavior. So we have done so many sophisticated tests, but beyond fitting data to a particular precise pattern is once you understood that, we are discussing A phenomena that is called scaling variable. What does it mean? It means that the system is self-similar, looks like itself at all different scales, and this has many implication, for example, even in understanding adoptions, right? Why there are different agents at different time, from the ind-individual investors to small banks to large institutions to maybe even nations, right? This is actually foreseen by the power law and is part of the theory that the different stages of a- The history of Bitcoin will be different agents, but the behavior stays the same. This why it's called invariant scale. The scale is the size of a system at different prices, different times in, or different level of adoptions, and it's the same, it's self-similar. And only the power law, by the way, as a function, is scale invariant. It's the only function with scale invariant. So it's not by chance. So on this," }, { "speaker": "giovanni", "time": "10:27", "start": 627.42, "text": "let's, I'd, I'd love if you could explain for people, because this has been a common thing in Bitcoin for a while Well, right? Like I came into Bitcoin, you know, early twenty thirteen, you were saying you were just analyzing things in twenty twelve. Especially at that time, there were a lot of people saying, \"Oh, it's an exponential, it's gonna grow exponentially,\" or the other one is, \"Oh, it's an S curve, right? That there's, it's, you know, we're, we're at the knee of the S curve and that we're about to really go through this big suddenly moment.\" Can you explain for us why you disagree with that? Why is Bitcoin not an" }, { "speaker": "stephan", "time": "11:00", "start": 659.92, "text": "Well, and, and all this is in the book, and if you don't mind, actually this could be a, an opportunity to show, to show you some" }, { "speaker": "giovanni", "time": "11:07", "start": 667.24, "text": "of" }, { "speaker": "stephan", "time": "11:07", "start": 667.3, "text": "the, of the, material in the book. the book is still in abwurda. Version, so it will, you know, it's going to launch soon, but I can show you some pictures and some ideas, so, you know, so for example It's actually explained almost immediately at the beginning of the book, where I cover these topics." }, { "speaker": "stephan", "time": "11:35", "start": 694.7, "text": "and it's clear Here it is, right? So for example, if you, if you show, one of the, the tools and describe these tools in details, okay? Here it is, and we can make this bigger so it's easier to see, okay? This one. Are you able to see it? Yes." }, { "speaker": "giovanni", "time": "11:56", "start": 716.21, "text": "Yeah, I can see it." }, { "speaker": "stephan", "time": "11:58", "start": 718.07, "text": "so Th-this is one of the simplest tests that one can do, right? If you look at the price in a chart where, the price is linear and time is linear, so you don't do anything, like many people use, for example, TradingView, and there is like a little setting where you can choose if you want to see the price in linear scale or if you want to see it, in, log scale, right? and with the tap A log scale for time, we have only a log scale for the price, right?" }, { "speaker": "giovanni", "time": "12:29", "start": 749.45, "text": "Right. And what you're talking about is having log in the, yeah, and the x-axis and log on the y-axis." }, { "speaker": "stephan", "time": "12:34", "start": 754.49, "text": "Right. That is the la- so we go through this transformation, right? Usually we start with this simple way of describing anything, right? I, in the book, I explained, for example, like somebody was taking a physics class, right? I taught many of these introductory physics classes. so- You are taking this class and, you have some data and you want to understand the nature of the data, and so we suggest in our physics classes as professors To start with the simplest possible assumption, right? The simplest possible assumption is that, you have a, a, some kind of a linear process, because in nature there are many of these, simple relationship between one quantity and another. So in that case, if you have a linear process, you will see a straight line by taking the, in this case, the price and the time, right? It will look like a straight line. And evidently, if you look at the price of Bitcoin, it doesn't look like a straight line in this graph. It looks- It's something like a J. Many people don't even see that because they see these huge big drops. It's part of the problem where are these huge bubbles that can confuse the data. But if you look at the overall shape, it looks like a J. The problem is not easy to distinguish between different type of J. Here I'm showing two different, processes. One is, an, the power law, and I show you also the exponential. The exponential is orange. The green is the power law, right? So you will now be able to distinguish between the two. Now, if you go and we do what you're able to do in TradingView, that is taking the log Okay, if Bitcoin was an exponential, it would be very easy test. Now, you can do more sophisticated test, but one of the things that I love a-about being a physicist, that they taught us to be very, very practical. So the eye can tell a lot of information about data even before you do all the sophisticated calculation, because that builds intuition. If you don't have intuition about the data, you can do all the sophisticated calculation, and probably you're going to do some mistakes. Stake, because you're not guided by a deep intuition above the data. So if I see, if I do this transformation of taking the log, but that is very important with Bitcoin, because that is usually, we do that when we have data that changes a lot of order of magnitude, and order of magnitude means, ten, hundred, thousands, and so on, okay? and Bitcoin went through these changes, because if you take a bit of history of Bitcoin, it went From few cents all the way to hundred thousand, right? So we're talking about several order of magnitude, right? When we change from ten hundred thousand cents log. So the log is actually ideal to look at a process which changes many order of magnitude. Because what the log does, the log gives you the exponent. So if I write hundred as ten times ten or ten to the two, the log base ten is going to give me that two. If I have thousand, it's going to give me ten times ten times ten, right? I can write thousand as ten to the three, it's going to give me that three. I can write ten thousand as ten to the four, it's going to give me that four, the log. So this why it's useful is giving me what is called the scale. So how, how the price will look like if, it was exponential, it will look like a straight line. And you can try that with, for example, gold, SP500, almost every single asset, if you take the log, is going to look over a long period of time like a straight line. In a log, what is called a log-linear graph, where you keep, you do the log of the y-axis and you keep the linear x-axis. In this case, got it. So just, just to" }, { "speaker": "giovanni", "time": "16:35", "start": 995.13, "text": "make sure I've got my understanding correct, and I believe Matthew Mazzinius has, has written and spoken about this idea as well, that kind of most of tradfi, so-called, go-- follows an exponential, but at a, at a low pace exponential, whereas Bitcoin is different, it's actually following a power law, which is a different thing altogether. Is that a fair way Way to summarize?" }, { "speaker": "stephan", "time": "16:55", "start": 1014.58, "text": "Yeah, yeah, very different mathematics. They are related, they are related, they are both non-linear processes, but they are very different at the same time. And, and so, yeah, and this, and many people associate exponential with fast growing, all of these other assets we discussed. They are exponential, but they are very slow exponential in comparison with, the power law. The power law, of Bitcoin is a power with six, and that is a huge powerful power law. Imagine a parabola, any- People say, \"Oh, the price went parabolic,\" and naturally they mean exponential, because many times when you have bubbles, the price is exponential, fastest exponential in that case. But actually a parabola, it's x squared, right? It's a power law with power two. Bitcoin is a power log with power six, so you can imagine how much faster than a power aula is. Very, very fast. It's a very fast moving J. Now This J looks like this curve, this green curve, right? That is a simplification, this is a very simple graph, but it doesn't remind kind of like the curve path that you see in Bitcoin when you plot it in a log-linear chart. Everybody's familiar with that, right? It looks like this, it looks bent, right? It doesn't look straight. Everybody's familiar with that, right? many people call it the rainbow chart or whatever, right? Because it looks almost like half of a rainbow or whatever. That is what happened to a power law when you take a power law and you do this log-linear chart. I don't know why it's continuing Okay, you know, it goes white once in a while. But anyway, so the, the problem with this is, you know, you know, if you do this to Bitcoin, you know what it is not, it's not an exponential because otherwise it will look like a straight line. So the question is what it is. And nobody was able to tell what it is because one, that is one of the criticisms of a power law is so simple of an idea, they say, \"Oh, anybody could have done that. Why they didn't do it?\" Because... Most people in finance don't have this idea of taking the log of time. They don't need to, because a lot of processes are more like exponentials and they don't are no power laws. In physics, we do that all the time. And believe it or not, I had almost arguments with, financial people in explaining that actually makes sense to take the log of time. they, they were so unfamiliar with it, but in the beginning, they even criticized that, and there is nothing wrong, because, you know, if I have a thousand days from the Genesis, block, that is how we measure time in this exercise, you know, basically we measure time from the creation of Bitcoin Then, you know, the log of time will simply be three, right? So ta-log of a thousand is three because it gives me the exponent that we discussed. So you can do it, the question is, what does it mean? It simply means I'm emphasizing the scale, I'm looking at the changes in the scale of time. So a change in, you know, from hundred to a thousand, hundred days to a thousand, will be one change of scale, from- From a thousand to ten thousand will be another change of scale and so on. And I do the same, same with price. And if I see a straight line in that graph, and this how the power law will look like, like a straight line, then I identify a straight power law. Now It's not the ultimate test, you would not just simply say, \"Oh, it looks like a straight line, goodbye,\" you know, and you close, and, and, and you're happy with that, you, that is a start, but If the data kind of looks like straight line, and you can see that with the price of Bitcoin it does, it immediately you can see there is a change, that curve that we usually associate with Bitcoin is gone, it looks straight, right? And once, and once you observe that You know that something important is happening, in particular if you know this, if you are familiar with power laws, one of the things that you will look at will be that You're covering a lot of orders of magnitude, right? And we power load those that we power load in Bitcoin does exactly that, and that people don't realize how difficult it is for data to behave in that way. You don't find that often, and in fact, when you find-- I mean, on one end you find it often because it's everywhere in the universe, in the other, in the other, just random data doesn't do that. You need to have some kind of very precise mechanism and process to create this kind of, behaviors." }, { "speaker": "giovanni", "time": "21:42", "start": 1301.96, "text": "So I guess the point you're getting at there is that there's an underlying sort of nature to it, right? That, similar as you have explained and Jeffrey West has explained, this idea that, you know, even the-- if you plot out the number of calories that an animal consumes and its size, that, you know, that's like a power law, or like the distance of the, you know, the planets from the sun, again, follows a power law. Yeah. Or the city Growth of the cities, that there are different network effects inside of a city, right? Whether it's the plumbing, the electricity, the roads, the, you know, the police, the whatever, the hospitals, that, you know, all these aspects are kind of growing together in a combined network effect. And I guess what you're getting at to this point is that Bitcoin itself is a network effect. It has a mining hash rate, it has adoption in terms of addresses that people are using to when they, when we spend and receive Bitcoin, and also the price of Bitcoin. And that's, that The underlying, there's a nature to it, and it's, it's following this trend of adoption over time." }, { "speaker": "stephan", "time": "22:40", "start": 1359.9, "text": "Correct, exactly. so yeah, we could have stopped there in the sense that once we find the power law in time and done a bunch of tests and show that it's a power law from all kind of point of, of view, you know, statistics, regression analysis, different type of, you know, you could lo-look at alpha with the data and project In the future, there are many, many different things that people that are professionals in the field know how to do. So the question is settled, you know, there is, it's-- and wh- that is one of the reason also we have a scientific Bitcoin Institute is because now we are in the process of- Of writing serious art-article that were-- because it's something that I should have done many years ago, but I instead I decided to connect with other Bitcoiners and, you know, the question should have been the other way around, why didn't I write scientific articles, books, etcetera, when I discovered this? Mostly because I wanted to share my enthusiasm with other Bitcoiners, you know? And I knew that this was an important discovery, but, I was also working In other field, I was very busy with my neuroscience research, with my, other career, with AI, at the time, and I put this on the side, you know? Now it's time because I, I'm doing this full time as a educator, as a researcher, and I want to distinguish this type of activity from what people usually do online, right? I'm, I'm continue to do that, but- It's one thing, it's gonna be" }, { "speaker": "giovanni", "time": "24:17", "start": 1457.22, "text": "supplemental as well as what we're doing online. So we" }, { "speaker": "stephan", "time": "24:20", "start": 1459.54, "text": "want to make it a serious endeavor where we want to engage other scientists, we want to bring academia to study this phenomena, we want to study if this thesis is correct that Bitcoin is a network and shows network property because, the connection between networks and power laws is explained very well in the book. There is an entire chapter dedicated to network theory and, and in, in that chapter we discuss As how, you know, when you look at actually real networks in life, the property of these networks are power laws, you know, the way, for example, that, the different- scaling of connections is called a scale-free network. there are big hubs like, for example, you, you are a big, huge hub with a lot of connections to the community, and then there are, other nodes in the network that have few connections, and if you look at, if you do a graph of, How many hubs there are with a certain given number of connections. So on the y-axis you have how many, of these Particular hubs you have with a particular number of connections, and on the x, axis you have a number of connections, it will look like a power law. My power law it goes down because you have a lot of, nodes with very few connections with-- and there are a lot, a very, very few nodes with a lot of connections, right? So, it's going to look like, power law like this. It's almost like similar to the wealth, of, so, et cetera. As in like wealth distribution in Bitcoin will also follow a power law. Is the point I'm saying that there are very, very" }, { "speaker": "giovanni", "time": "26:08", "start": 1567.81, "text": "few whales who have, you know, a thousand coins or more or whatever, and then all the way down to, you know, shrimp and a smaller number of, you know, people, holders, right? So" }, { "speaker": "stephan", "time": "26:17", "start": 1577.06, "text": "to, to, to make it more clear one more time, so the Y-axis you will have how many of these, On the right, so the percentage also, that have a particular, number of nodes and then here the number of connections, right? So on the, on the right you have nodes with a lot, a lot of connections, but they are few, and the ones that have few connections are a lot of them, right? But we are not that is makes sense, but The fact that it follows a very power law, very precise power law, is not trivial, and it has been, in fact, the theory, the world theories about networks, they didn't predict at all that this is the type of distribution that you will find. The, the theory The existing theory before people actually went and did the observation, fatta, the first big observation was from this physicist called Barabasi, and Barabasi studied the internet among all the possible network, the network of network, that is the internet, and he was very surprised when they actually measured in a very precise empirical experiment this particular distribution, the Zipf law power law, and then they needed to explain it, they needed to come up with Theory that was able to ex-p-explain this distribution, because there were some theoretical papers in the past previously that say, \"Oh, it's, you know, given these conditions, you will expect a Gaussian distribution, but it's the tip-typical distribution that we observe, in, hi-height, for example, right? So if I have height, there are very few people that are very short, there is an average number of people that are- Going to have some, you know, there is a, the majority of people are going to have a, an average height, and then very, very few people that are very, very tall, right? And as you go away from the average, you have less and less people that have very big height, right? And this type of distribution is very different from a distribution that looks like this. But this is what the theory said, and then when we observed, this why physics is the queen of sciences, because it doesn't matter Your assumption, you go and you do the experiment, you observe first, so it doesn't matter if you assume that Bitcoin is exponential or maybe it doesn't follow any pattern, you go and you do the experiment, you do the measurement, and when the measurement, when the data tells you something, you listen. It's no, there's no debate, you know, you can debate the technical, Quantities, right? Is it, this R squared calculated in this way? We should maybe calculate it in this other way. Now, there is no doubt that Bitcoin is a power law, you know? and we will see when we actually try to publish the paper, which kind of feedback we get from the community, you know, of-- This is why we want to go through the peer review process, you know, and see if we actually can publish these papers in journals, right? You know, physics journals and such. But, I'm pretty sure that there is no doubt. When you look at the data, it's very difficult to throw away the data saying, \"No, no, no, it's an artifact or it's a mistake or you didn't, you know, consider this.\" Yeah. Now, I guess" }, { "speaker": "giovanni", "time": "29:45", "start": 1785.33, "text": "while we're on this topic, I think the other big question that listeners might be thinking is, while we're talking about this concept of, you know, Bitcoin following a power law, right now the price, as we speak, is about seventy-one thousand dollars, and some people are saying," }, { "speaker": "giovanni", "time": "30:01", "start": 1801.1, "text": "In the book, in the draft I looked at, you mentioned certain falsification conditions. So you mentioned a sustained period of daily close below the lower corridor, statistically significant shift in price power law exponent, failure of three law consistency, a sustained collapse of hash rate or adoption reversal. So can you just explain a bit from your perspective what would it mean to actually falsify the power law for Bitcoin? Yeah." }, { "speaker": "stephan", "time": "30:25", "start": 1825.22, "text": "So we talk about falsify because I want to people to accept this idea that we- Bitcoin has a very structured growth over the long period of time, and I want to remind, when we are talking about long term, we are talking about years, right? So we're not talking about changes in the price on the scale of months or days. That is not what the power law is about. It's about this very long term trajectory, and it's important because, you know, we don't know, right? So if I tell you Bitcoin is going to be one million dollars in eight years It's very different from somebody telling you Bitcoin is going to be a million dollars in two years, or it never is going to reach, one million, or it will take a hundred years, right? So even if these are very long term trajectory, knowing more or less the In a number of years, let's say, it's a very important contribution, right? In this way, it give us an understanding of where Bitcoin is going. Now, the idea of falsifying, so every theory, every scientific theory, and this is a-- and every time I talk about it, comes to my mind, oh, maybe I should explain what a scientific theory is in the book. Maybe we need a little box for that, right? Because I'm trying to be addressing this also with people that maybe aren't super familiar with the scientific genre, but different From how we use theory in our normal language, where, why, this is ju-just in theory, right? This in theory should be like this, and many people mean with that, that is kind of like a guess, right? But in physics or in science, a theory is not a guess, it's like the opposite. It's actually the apex of our scientific understanding. It means it's the most complete, most structured understanding of something, right? And the theory usually has some tenet, like for example, the theory of evolution. You have some criteria, that can be used to be falsi-fa-- to falsify a theory, and make-- and the theory needs to make predictions. It's fundamental because if you have a real deep understanding of something, you should be able to predict something that was never thought before and that-- and is a consequence of the theory. and so this is why I came up with this falsify criterion, and the idea is that it's not, it's that we have to be a little bit careful because on one end, I think it will be A misunderstanding that if we don't follow a power law anymore, the power law was never true. It's not the case, because I think we can come up with a lot of tests to show that up to now, Bitcoin has been a power law, has been scaling linear, has followed a very precise pattern. That is very, very difficult to dismiss. What many people are interested, of course, is the future. Can the power law continue to be valid in time? And so it's not really falsifying what we have so far, but actually showing that there is something different, right? But I try to simplify, and so I use this word falsifying. So it's very important to make this difference. But yeah, so I think the most important test is this, because we are talking about a dynamical process, we're talking about how Bitcoin goes there. So it's not so much important where we are. So for an, for example, right now we are A little, you know, we are so far, so somehow away from the long trajectory, right? So the long term trajectory that usually when people draw these charts, they show this line that is kind of in the middle of these big, huge oscillations. Many people think that is the power law It's just one way of expressing the power law. It's not really the fundamental power law. The fundamental power law is the process, so it's basically how we go there. Recently I made a nice visualization of this. I show all the different slopes that is basically where locally we are moving, right? So when we have a, a bull run, for example, these local slopes, this daily slope that is the power law, calculated in terms of the difference between one day To another, right? They look wild. Some of them, they look very, very, very different from the usual direction of the power law. They look, they look much steeper, for example, and they look like they are pointing up. When we have a bear market, they are pointing down, and sometimes very, very fast, right? So in a certain sense, it's almost like you are comparing the position of an object with the velocity. How you go somewhere depends on the velocity. Right? And both the size of the velocity and the direction of the velocity. Guess what? When you average all these wide arrows, I saw I made a beautiful graph where you see all the different arrows. When you average all these, like almost like the wind, like the local wind, where the wind is blowing for Bitcoin, you get the power law. And you get it as a dynamical process, not as a position in the chart, right? Not as a point in the chart. That quantities also can be used as a test for the validity of Bitcoin. In fact, probably is the most sensitive test, 'cause it turns out the slope of these vectors in the average has the total trajectory of a power law. And we have a precise distribution, so it's actually, it's a beautiful thing because they both show Bitcoin as a long-term trajectory, but also describe these changes. Relative to this long term trajectory. I did tests where I not just measure, you know, the average value of N that is oscillating, but is oscillating around a particular average value, but also the shape of this distribution, how big these deviations are. These deviations are stable at least since eight years, and previously the deviation of itself were actually smaller relatively to now. Something happened in two thousand and thirteen where the distribution became a little bit wider, so we had actually more volatility in a sense. So many people associate vol-- associate volatility, think about the Bitcoin volatility as decreasing in time, but that is absolute vol-- volatility. If you measure The volatility relatively to the slope itself, so basically the change in price, then it's actually stable and has been stable for more than eight years. It's a really incredible result. Actually, we have very sophisticated tests to measure if we change this power law, and so far, we haven't. Even this distribution is the same. So basically, Bitcoin has done the same thing over eight years, at least from a dynamical point of view. So this is one of the best tests. Now, I did mention the floor, because the floor is something that it's easy to understand, more-- and people are very worried, right? They see the price going down, they want to have some kind of relief, they want to s-- know that maybe we reach a particular place and we stop there, right? And historically, this is exactly what happened. But it's this weird floor, so if you take the general direction, and then it's very important to s-- also to explain But this applies mostly if you use the dollar, for example. And why the dollar? Because the dollar is what people use worldwide as, you know, the currency, right? Like the global currency. They don't use gold, they don't trade using gold, right? So many people mention the same floor using Bitcoin Express in terms of gold. Bitcoin Express as in terms of gold is still a power law, but that floor is less meaningful. And I will explain you in a moment the meaning of that floor. So there is this floor that historically has never been violated, even by the COVID, when we had the COVID crisis, the price arrived to this floor and then bounced back. It's really fascinating to watch. The, this floor is about sixty percent deviation from the general trajectory. Now, it can be calculated in other ways. For example, you can take hash rate and you can do a model. We know there is a relationship between price and hash rate, and we can use that to make a model of the price, and you get more or less the floor. And you can also calculate the cost of production, that is a little bit more complicated formula, but involves the hash rate, and guess what? You will get the floor. So the floor seems to be associated with the cost of production of Bitcoin. So this why probably has been never- Over violated because, once the price are right there, is already the market is already exhausted, the miners stop selling because they don't want to lose money, they'd rather keep Bitcoin at that point, maybe take loans or whatever. So this why we need Basically historically never went below this floor. So I used it as a secondary measure of falsification of a model, right? Yeah. If we see that we're falling below this level, and just for" }, { "speaker": "giovanni", "time": "39:51", "start": 2391.03, "text": "people to understand, like the context today, like can you give, like, just rough numbers, where is sort of, where would you say the power law is today, and where is the floor today, roughly? So right" }, { "speaker": "stephan", "time": "40:00", "start": 2400.03, "text": "now we are seventeen, I say floor is more like fifty-five, for example." }, { "speaker": "giovanni", "time": "40:06", "start": 2405.82, "text": "Yeah." }, { "speaker": "stephan", "time": "40:06", "start": 2406.28, "text": "And so if, we violate the floor, and it doesn't have to be like a week, right? Like there is a, like a very sh-fast, violation and then we go back. That is not. It needs to be an extended one. It needs to be," }, { "speaker": "giovanni", "time": "40:22", "start": 2422.11, "text": "right? On the order of months. We would have to go below fifty-five and then stay below fifty-five for a long period of time, for" }, { "speaker": "stephan", "time": "40:28", "start": 2428.19, "text": "maybe at least a couple of months, right? And then, yes, then I will say something is wrong here, something is different. Isn't that? Power law isn't true because it's been true, it's something different. It's something different system, you know, it's almost like a patient, right? You have these long-term power laws about the growth of a task, right? In an elephant, for example. You look at this trajectory, you look at all the other elephants, they behave in this way, and then there's an elephant that for some reason doesn't follow anymore this power law. It follows up to a point and then it doesn't follow. Well As a scientist, you look at this and say, \"Well, something changed with the elephant. It doesn't get anymore. Is that change maybe it's sick? Maybe there is some kind of illness in the elephant, right? Something happened in terms of a mechanism that may-- It's not that the idea that the power law, the task follow power law is wrong, is this particular elephant that went sick. Yeah. So I would say this is exactly what we thought. And then I guess while we're" }, { "speaker": "giovanni", "time": "41:32", "start": 2492.13, "text": "there, I guess it's probably a lot of people will be interested. What about, To the upside. Like, is, is there a similar kind of question there that if Bitcoin just kind of rocketed up crazy high and stayed high, right, would you, would you make the same argument?" }, { "speaker": "stephan", "time": "41:46", "start": 2505.78, "text": "Right. So again, this is in the other way. In that case, we don't have a floor, so we really have to use something like this, and Test, right? This test of a slope. So if we start to see that the, average value of a slope goes up and up and up instead of being stable and oscillating around a particular va-average value, it starts to go up more and more and more. And I actually, I should actually add this to the book. I will never finish the book if I start to add more and more stuff because I remember I made a post long time ago where I had different scenarios with this test. And I was Showing the different type of scenario, it was a scenario where we had an exponential growth, and you can pick it up, this test can pick it up almost immediately, and it's actually a visual test, you will see these Value that right now if you plot it simply oscillates, right? It goes up, it goes down, but it oscillates around an average value which is about six. If this value starts to go up and it became seven, eight, nine It's not a power law because power laws are supposed to have this value stable, you are measuring something else. You are, you are thinking you are dealing with a power law, but now it's behaving more like an exponential. And so that will be a very sensitive test to show that, yes, Bitcoin is not A power law anymore is becoming something else." }, { "speaker": "giovanni", "time": "43:11", "start": 2590.81, "text": "Yeah. And while we're there, I guess the other question people will have is, what about, you know, maybe in the long run, maybe twenty years from now, who knows, does the world eventually hit a quote-unquote saturation point, and then like basically most people have adopted it, and by then, like, would, would things change then? Like, let's say in twenty years' time, Bitcoin is, you know, ten million dollars a coin, and most of the world has adopted it by then, does the power law still stay then or" }, { "speaker": "stephan", "time": "43:38", "start": 2617.97, "text": "Yeah, yeah, yeah. So, sorry I'm losing a little bit my voice, but, so that is an another important topic, right? And the way to address that is this, so people understand more deeply what I'm talking about. If you understand how the scaling processes work, one of the reasons why I hope that we continue to behave as a power law, because many people, maybe they don't like if we break down, right? I saw some people celebrating Even the idea that we could break down simply because maybe they simply want to show that I'm wrong or this idea that Bitcoin follows a precise pattern is wrong, so they are right. So if they can go, can break down, maybe can break up, and but they still won't be breaking up, right? Because they hope they become, become exponential, and I have insisted so many times saying even that will not be good, because most exponentials grow up fast and then they collapse, right? That is Fiat- stable," }, { "speaker": "giovanni", "time": "44:39", "start": 2678.93, "text": "or they're less kind of--" }, { "speaker": "stephan", "time": "44:40", "start": 2679.89, "text": "Exponentials are associated with fiat behavior, and it's so beautiful that Bitcoin isn't. In fact, I have this one of my reports that got- More like ever in the history of my posts, there's been this post where I do this scaling test, where I show-- I can even show you this graph if you want, in a second, where I show how different Bitcoin's behavior is in terms of the scaling property from NASDAQ, gold, everything else, right? It's so visual that really people liked it. I'll show you the graph in a moment so we can discuss it. It's also in the book." }, { "speaker": "giovanni", "time": "45:18", "start": 2717.78, "text": "Can you just explain a bit more about this saturation idea?" }, { "speaker": "stephan", "time": "45:21", "start": 2721.04, "text": "Yeah, yeah, I'm going there, I'm going there. Believe me, I know step by step. So the idea is this, right? When you have power law, the essence of a power law is that as we grow, we slow down That is the beauty, and this why is also the favorite growth of nature, because as this elephant grows and it needs to have a bigger and bigger task, if it went exponential, it will consume so much energy, so much resources, but something will goes wrong. Just to give you an example About saturation, imagine a, a process where there are some algae or some bacteria, right, in a lake, and, and, and I caught sailor doing this example, and I told him, \"I'm sorry, sailor, you know, you do a lot of wonderful thing for the community, but sometimes you don't use the right analogy. You're talking about an exponential process when you should talk about power laws, right?\" And what he was talking was this. Doubling, he wanted to show us how fast exponentials are, and then implying maybe coin does that, right? So the idea is this: imagine I have a, a bacterium that is, doubling every five minutes. Every five minutes you start with one, then it becomes two, and four, then eight, and so on, right? It doubles every five minutes. And there is this lake or this container, whatever, where it lives, right? And there are nourishment, there is nutrients for, for these, living Structure of a living being. When, when he arrives, ima- imagine that he took a month, right, or five months or whatever, you know, to feel fifty percent of a lake Well, the question is, how long will it take to fill the rest? So it took one year, let's say, very long time, to fill fifty. How long will it take to fill the rest? Remember, it doubles every five minutes. Do you know the answer? I don't want to put you in a bad spot, but it's a pretty simple-- No, I don't know. It's one of these tricky questions. Five minutes, because remember, it doubles, right? And it needs to cover the next, right? The next fifty percent. So it will take only five minutes. So it took one year to cover fifty percent. The rest of the fifty percent is going to be filled in only five minutes. That doesn't happen with power loss. Because what, you know, the, the, the bad things about filling the lake is that now you don't have any other space to grow, right? You die out. It's the only thing you do. There is no nourishment, there is no place to go. The only thing that can happen is that the colony start to kill itself. And that is what happened with a lot of exponential processes. They grow fast, they use all the resources, they're" }, { "speaker": "giovanni", "time": "48:05", "start": 2884.73, "text": "unsustainable. That's the point. They grow so fast that they're unsustainable. With the power" }, { "speaker": "stephan", "time": "48:08", "start": 2888.03, "text": "law, what you will see is that it- Takes longer and longer to feel the next step because what happened is still growing and relatively fast, but everything slows down." }, { "speaker": "giovanni", "time": "48:20", "start": 2899.63, "text": "It's like a diminishing returns kind of idea. Exactly." }, { "speaker": "stephan", "time": "48:23", "start": 2903.32, "text": "but, you know, this looks kind of bad, the diminishing returns, right? Because it seems a negative thing, but actually it allow the system to adapt to the environment And this is what happens with Bitcoin. If we want to have a Bitcoin that is going to exist for the next twenty years or longer until it becomes like a million, ten million, we want exactly to grow as a power law. Now, in terms of your, the question that you answered. So once you start to play with the number, you realize, for example, that every time we double the size of a system in terms of people that adopt the system or entities, they can be even AI's or whatever, the price goes up with the square. And then you say, okay, how long does it, you know, how long does it take for the price to reach, let's say, ten million? And the power law gives us an answer, it's going to be around twenty Twenty years, around twenty years. And then you realize that to reach a price of ten million, you-- and that, you know, right now let's say we round it to hundred thousand, right? We are in the neighborhood of a hundred thousand. So that means a change in price of hundred. And then you realize, because of that square factor between a, you know, the number of people in the network and the price is a factor of square, that you only need ten times more people. So we need ten times more people that we have right now to get-- and these people can be represented by ETFs, right? An ETF is like a big, huge whale that represent-- It's one entity, but it represents thousands of people, right? So the network needs to work By a factor of ten in terms of adoption to get the price a hundred times. And then you can ask the question and say, okay, well, many people have adopted Bitcoin. Almost everybody agrees that it's probably around a hundred million. There are many different way of measuring that, but close around two hundred million. So even if you multiply that by ten You're going to get a billion, but it's very, very far, at least a factor of ten, relatively to the population now. The population in twenty years probably is going to be even bigger So we are far away from saturation. And if you talk about maybe, AI agents using Bitcoin, et cetera, so you can see the possible people or entity that are using Bitcoin are very, very far away from these numbers, right? One billion users, for example. And that will bring us already to a price of hundred. A ten million dollars Bitcoin, and that means if you translate it in terms of a, market cap, it will be a market cap of at least two hundred ten trillions. Well, you multiply that by another factor of two, and it will take just a few more years, you know, maybe four or five years to get A factor of two more, then you are talking about the wealth of entire world. We are talking about close to five hundred trillions. It is close to the wealth of everything, real estate included, you know? So probably at that point is when I'm expecting something to happen to the power law. And, and it will be something dramatic. It will not even be some kind of a saturation, simply because we are running, you know, against some of the limitation economic The limitation of the world, unless something big happens where productivity goes to the stars, because maybe even literally because we start to go to mine asteroids by that time, AI is going to be so much, is going to increase productivity so much that, these limitations that we have right now will seem You know, nothing in comparison with what we can create or produce in twenty years from now, you know, because people undervalue the revolution of it that I represents, right? But this is-- and, and I discussed this in the book, and I say, \"Listen, if we can...\" Predict the behavior of Bitcoin that according to this reasoning, isn't going to saturate, isn't going to saturate at least until it reaches ten million dollars, because we only need a billion people, so we're not, not running out of people at all." }, { "speaker": "giovanni", "time": "52:50", "start": 3169.92, "text": "Yeah. And I guess to your point earlier about power law distribution, even at that point, it might be the wealthiest one billion people on Earth who have, you know what I mean, like because it might be a disproportionate, like even though it's like not the full ten billion or whatever at that point, who knows how many people, but it might be the richest one billion out of the ten who have Bitcoin, you know, so that, like, that it just represents a larger share of the actual- You know, let's say people who have wealth, or serious wealth, let's say. The" }, { "speaker": "stephan", "time": "53:19", "start": 3199.46, "text": "institutions also, right? Because our-- This is where we are switching now, bit from individual investor to large institutions that represents a lot of people, you know, and now nations like they behave like whales in, in the network and so on. We don't see any signs of, saturation because actually some of-- these are some of the sophisticated mathematical tests that they did, because this why I wrote an entire book, and the book doesn't even contain one tenth of all the different tests, the different calculations. So for example, there is this group of scholars that they studied, kind of what Barabasi did, by measuring all the links in the network, they actually studied other network, because, at that time, they had mostly the internet Net as a real example of a large network, but now we have many of them, like, for example, there are these, scholars, Chinese scholars that look at, Weibo, WeChat, and many other real life networks, and they found out that both the nodes And the links in these networks, they don't grow like exponentials, they lo- they grow like power laws. Which is in fact, you know, and that is one of the recurrent debates that we have in the community, that people mention these S-curve, and I have a like- Entire sections of a book where they explain carefully what is an S curve, how it's derived. An S curve is nothing else. So you start with a distribution that looks like a Gaussian distribution, right? Because you have a early adopters, you have innovators that come later, then you have a early majority Late majority laggards, right? And it looks, the typical, distribution of adoption looks like a bell curve, like a typical bell curve, right? That we discussed, similar to what you will get if you look at the distribution of heights in a population, okay? And may-- and if you sum, so the, the technical term is integrate, if you sum All these people in this distribution, guess what? You get the S curve. This is where the S curve comes from. And many people use that because they say, \"This is how this, how the adoption looks like, right? It starts low and when it reaches the majority, the early majority starts to go very fast up, and then there is saturation, so it looks like an S curve, right?\" Bitcoin doesn't follow that. Because even adoption, it's a power law. And these people, they studied real network, I mentioned this paper in, in the book, they study all these real, for, for example, it turns out that even the internet exactly works like that, is not an S curve, because usually this S curve is associated with physical things like telephones, for example, refrigerators, or the car, the bicycle, and so on. When you look at social network like, in- Internet because people started to accept the Internet because other people are on the Internet. Let's go, it's a social phenomenon, social networks, both the links and the nodes follow power laws. And they studied, they even developed a mathematical tool, to- You basically start with a very broad equation, very general equation, and we say, \"Assume that this equation can, if I change slightly this parameter, it can become an exponential, it looks like an exponential. If I change this parameter, it looks like, one of these.\" Curves that saturates like one of these S curves, and if I change this parameter, it looks like a power law. And we run it with the data, and we calculate these parameters, which parameter it is, and we found out over and over again that the parameters that we found show that the process is a power law. I did exactly the same. Yeah, that's a fascinating" }, { "speaker": "giovanni", "time": "57:16", "start": 3436.43, "text": "insight. I think that's a really good spot to finish up and have a takeaway for people, which is that, you know, Bitcoin is following a power law, and as you said, that's actually a good thing What many people might want is, oh, they want the exponential, they want the S-curve, because they feel like it's gonna grow faster. But the challenge with that is, it's not sustainable. I think that's kind of, in a simple way of understanding it, that's, that's what it is. So, you know, we've hit about an hour, so let's leave it there. I know there's a lot of other questions I have, but, you know, we'll, we'll keep it, manageable for listeners. But just before we let you go," }, { "speaker": "stephan", "time": "57:56", "start": 3475.97, "text": "Book, it's on, on Amazon, so you can look for our Physics, of Bitcoin. Now, we have a website that is called, is altogether vphysicsofbitcoin dot com, and it's actually a very nice, website because it's going to be a companion where it'll be, like mini lectures where people can fa- can follow, where it'll be live charts, you know, it's going to be a very nice reference for anything related to the power law. And for the institute, it's, again, all together Institute dot org so they can look for it, and again, it's going to be very useful website because we want to be also a hub for learning, maybe, maybe courses over there that we offer to people for free about Bitcoin, about, all the ideas related to this complex system. So we're trying to create, all kind of resources for people to understand better. The beauty, the mathematical beauty and the significance of the studies that we do. Yeah, look at these two. Well, listeners," }, { "speaker": "giovanni", "time": "58:59", "start": 3538.56, "text": "make sure you check it out. I'll put the links in the show notes at scientificbitcoininstitute dot org and thephysicsofbitcoin dot com. Listeners, make sure you share this episode so more people can learn about Bitcoin as a power law. And, Giovanni, thank you for joining me today." }, { "speaker": "stephan", "time": "59:11", "start": 3550.99, "text": "My pleasure, my pleasure." } ] }