Natalie Brunell
Physicist Explains the Certainty of Bitcoin's Future Price
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Physicist Explains the Certainty of Bitcoin's Future Price
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- Power law predicts that Bitcoin will be close to a million dollar in eight years. 20 years, that is when actually Bitcoin will be $10 million.
- >> How sure are you that that's going to happen?
- >> I would say close to 90%. Almost all corporations die within 150 years.
- >> But what does that mean for corporations that are backed by Bitcoin? Could they live forever?
- >> Exactly. But this is one of the reason why I want Zoro to start adopting this language of a Pablo because he could say exactly that. We are turning corporations into cities.
- Hey everyone, before we jump into today's conversation, I want to give you a heads up. My guest is a very well-known physicist, Giovanni Santastasi, and he gets very deep very fast. So, I want to take a minute to explain the big idea behind this episode
- before we dive in. It's called the power law. And here's the simplest way I can explain it. There's a pattern in nature that shows up pretty much everywhere.
- Cities follow it. The human body's development follows it. The internet's adoption follows it. And it's the pattern of things that grow slowly, steadily, and end up basically indestructible. Rome has been around for
- thousands of years. Cities survive wars, plagues, disasters, and they keep growing. That's the power law. Now, compare that to most things that humans build. A company has a hot product, scales fast, peaks, and then kind of
- fades away or dies. The average company on the S&P 500 today lasts less than 20 years. That is not the power law and we'll explain more in the conversation.
- So why do cities last and most companies don't? Because cities are networks that grow organically mostly bottom up.
- Millions of people freely choose to live there, build there, trade there. There's no single point of failure. And the more people who join, the more valuable the whole thing becomes. That's why cities don't burn out. They compound. Now, you
- already know Bitcoin is a network, but here's what's even more interesting. My guest has studied Bitcoin's price chart for years, and he found that Bitcoin isn't just any network. It's growing like a city. It is following the power
- law. And over the long arc, more than 15 years of data, Bitcoin has tracked this pattern with stunning accuracy. Now, in the short term, Bitcoin still goes up and down. Wars, banking crises, market crashes, those move the price dayto-day.
- Giovanni calls those oscillations, like the weather. The power law is the climate. It's the long-term path the price keeps coming back to. And here's why people are paying attention. The power law points to a million per
- bitcoin in about 8 years. And $10 million per Bitcoin in 20. And Giovanni puts it at 90% confidence that's going to happen. Not because he's guessing, but because the data has held up so far.
- So keep this in the back of your mind as you watch. Companies die, cities live forever, and Bitcoin is growing like a city. Let's dive in. Hey everyone, welcome back to the show. Joining me in
- person is Giovanni Santosi. He is the director of the Scientific Bitcoin Institute and he's famous on X for talking about Bitcoin's power law. So, Giovanni, thank you so much for joining me.
- >> My pleasure.
- >> I'm excited to chat with you. I I watched some of your interviews and I have to be honest, some of it was a little over my head. Um, you know, you're a scientist, a physicist. So, I think we're going to simplify things for
- for the purpose of our show. Um, so maybe let's just start with the power law. If you had to explain it in a sentence, what is the power law? And then we can break down how it applies to
- Bitcoin.
- >> Okay. So, it's actually a formula. Uh, it's called power because uh, you know, if you remember from high school taking the power of something, right? For example, if I say um, usually we study the parabola, right? It's an equation
- that says y equ= x². Correct? That x² is the power.
- >> Okay.
- So, a power law is a relationship of that kind. But it doesn't have to be two. It can be any number. It can be a number bigger than one. It can be a number less than one. It can be a fraction. It can be 1.56. Whatever, right? Um and so there are it seems kind
- of a trivial thing, right? There is such a simple equation but there are many equations like this in nature. In fact the majority of a laws this why it's called law uh in uh in nature like
- gravity um how much light we get from this uh light source for example is proportional to the temperature fourth to the fourth power. Same thing with the sun. You look at the sun there is a a
- certain temperature. The temperature of the sun is proportional to temperature to the fourth power. Wow.
- >> Um if I double um the light of the sun, you know, if I double the temperature of the sun, if the sun was two times hotter, now you don't get two times the light, you get two to the fourth power.
- So it's 2 * 2 * 2 * 2, right? So it's 32 times. Um so um doubling the temperature of the sun gets 32 times more reli. And there are many relationship of these
- things. You can see it's nonlinear, right? because if it was linear you double and you get two times whatever right in this case more light if I in I increase the temperature but it's not just two because of this power you get
- 32 with bitcoin we found a similar relationship where you have the price is proportional to the time so it's just a function of time it is actually an interesting thing right because we always say the bitcoin is time we have
- all this idea in our head about what bitcoin is or some of the property But the power law is actually the mathematical expression of that. So it's a formula that says the price is equal or proportional to the time. So the age
- of bitcoin how many years you can measure it in days, you can measure it in years. And then you take the power and that power is 5.8. So a number close to six.
- >> Um so it's very interesting that there is one simple formula. Now, of course, there are oscillations around this formula because uh Bitcoin is still random, right, dayby day. But the
- long-term trajectory is actually a simple formula.
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- Does power law essentially explain something's growth, something's adoption?
- >> In general, um these power laws describe some property of a system. This this property is very fundamental. So I have to be a little bit technical. So the it's not just a curve like another. is
- this why so many laws in nature are of these very simple form but there is something very deep about how things grow when they grow as power laws what let's explore them a couple of them
- right the first one is if I describe this curve right for example everybody's familiar if I look at a linear graph of of a bitcoin is going to look like a J right yes there are these big
- oscillation due to the bubbles but in general it looks like a J it goes up.
- There is another process that looks like a J that he says is called exponential.
- A lot of for example inflation is exponential and you get that process when you have some kind of rate of growth that is constant in time like a bank account. If I compound like imagine I have a bank account that gives 5% a
- year. I compound that interest over the years the gains in this uh bank account and you know it will look like a J in a graph like this. Now if I take that J
- and I take the logarithm what is the logarithm is a function think about like a little box where I put something in and it gives me something out right this box what it does I put a number with a power let's say >> 100 right I can write under as 10 * 10
- or with what is called the scientific notation 10 to the second right 10 time this is what it means if I put this number inside the logarithm the logarithm gives me that exponent that two. So I put in 100, it gives me two. I
- put a th00and 1,000 is 10 * 10 10 time 10 time 10 time 10 time 10 times it gives me three. You see how it works?
- It gives me that exponent.
- >> Okay.
- >> Now that that exponent is very important. We call it scale at the scale of a phenomena. So if I have a phenomena that is on the order of 100 that scale is two. If I have a phenomena that is on
- the order of a thousand the scale is three and so on. And you are familiar with that scale because for example when we say a earthquake was of a richtor scale three this is exactly what is meant is this exponent because if I go
- from a earthquake that is a scale three to four the change three and four the same you know similar right four maybe is few% bigger than three but actually
- the change between three and four indicates a change in 10 in the amplitude of these waves.
- >> Yeah, it's a huge difference. It's a big difference in an earthquake of let's say scale maybe five it's maybe destructive but one six is really devastating right so it's 10 times bigger so this is the
- scale what is the re relevance of that if I take the logarithm of the price of bitcoin only on the y scale everybody's familiar with that curve right it's not a straight line it looks like a little curve like this everybody that's look at
- bitcoin charts on a regular basis is very familiar right almost looks like a rainbow something like that right it curves. Now if it was exponential if it was one of these other processes that we found often in nature where you have
- something that grows like for example if I have a bacteria in a a petri dish I start with let's say one bacteria that bacteria splits in two then these two splits in other two and so on. This process uh is an exponential process and
- is very interesting because u uh imagine I have a a bacteria that doubles itself every five minutes but it takes uh let's say two days to fill 50% of this dish right this petri dish it will take
- another five minutes to cover the rest of the 50%. So maybe it took five days to arrive to 5%. But uh because of this doubling the other 50% is covered by only five minutes. Okay. Grows very very
- fast. Uh you can see me that in fact one time sailor I I love sailor right because he's also an engineer. talks about physics but sometime I wish he talk the understood more of a power law
- because one time he made this analogy with analogy in a lake right and he was talking about exponential growth but the beauty of bitcoin it doesn't follow this growth because what will happen imagine we are close to saturation with bitcoin
- as it grows right maybe a lot of people have adopted bitcoin well if you do the next doubling step then the system dies because there is no room to expand right immediately covers everything. What
- happened to that system? He dies because he doesn't have any more food. And in fact, there are many of these processes like um there is this famous physicist called Jeffrey West that he wrote an entire
- book that I suggest everybody to read.
- It's called scale. By the way, I mention the book scale and I describe it in my own book that I tried to do a little bit what scale is about but apply to Bitcoin. uh because this book scale explains the importance of this power
- laws all over the nature in our physiology uh in the universe in uh economy everywhere where these power laws show up everywhere. So it's very interesting book to read because it opens kind of
- your mind about understanding the universe through this idea of scale that is a very important concept and uh when you apply to bitcoin if you take the logarithm of the uh y and the x you know
- so I don't take just the logarithm of of a y but also x all of a sudden something almost miraculous happened that curve that we are all familiar becomes a straight line.
- >> It becomes a very simple beautiful straight line. It's almost scary when you see it in a in a picture, you know, like for example, I can show it in the book.
- >> It looks like this, right?
- >> I put it in fact actually in the beginning of the book itself. So I straighten up. It looks like this.
- >> Okay.
- >> Of course there are still the oscillations and maybe we can show to you can take a picture. Um but uh you see there are these oscillation but it's not very interesting like for example in
- the show what uh uh Bitcoin did they show this chart and they called it the chart that you cannot unsee because all of a sudden you see the complication of Bitcoin became something simple it looks
- like a straight line roughly right and you can draw a straight line through the price we don't draw it by hand we use a mathematical method that is called regression and that regression calculation gives you two things. It
- gives you the slope of that um line and that slope is six 5.9 something like that. Uh do you remember when I told you the formula for the price is nothing else than time to the power of 5.6 six
- something like close to to that value almost six you can round it to six and and it's interesting because first of all there is only a simple formula that describe a price and then that six has a
- meaning it like for example a famous another famous power law that I describe in the book uh is called clever's law it describe a relationship between the how much energy an animal consumes
- >> and uh the mass of the animal and so I can make a graph where I have a mass of a animal on the y a on the x axis uh the energy so the human being for example uses almost 100 watts that is basically
- the energy of a pulp you know this what we use to survive and then you put all the different animals with that much energy right from the mouse to the elephant by the way it works with insert it works even with cells it's called the
- clay's law and if you plot the log of a mass and the log of a energy you get this beautiful straight line that connects all these animals >> and that means it's a power law.
- >> It's a power law and the slope of that power law is 3/4. So what is the significance of that for that require it's almost like the fingerprint of that phenomena that we are describing in the
- case of the animal it means if you double the size of animal the animal doesn't consume two times the energy it consumes only 70% 1.7 so it doesn't go to two it go because of that power right
- you have to take two to the three quarter but it gives you a number that is smaller than 1.7 so there is a discount of 30% % of energy.
- What is the concept of that? By the time you go from the mouse all the way to the elephant, the elephant instead of consuming 10 times more energy that if if it was linearly because an elephant
- is about uh 100,000 times bigger than a house, let's say, and instead it uses only 10 times 10,000 times more energy instead of 100,000 because of that recorder.
- >> Interesting.
- >> And uh so there is almost a discount of 10. So the elephant will not even exist if it was not because of this power law.
- If it wasn't exponential, right? Imagine the energy consumed was going faster and faster up. Probably we will not have animal maybe even not even human beings because by the time you go to that size you will consume so much
- energy. So this is a almost a um scaling in energy right there is some kind of uh saving associated with this scaling and nature locked in in this
- process choose this process rather than something else because it optimizes how to scale animals and make them bigger and bigger and bigger. Yes, you pay a price you consume more energy but not as much as if this relationship was linear.
- So this three quarter is useful.
- >> Okay, >> with Bitcoin that number is six. That is the fingerprint of Bitcoin. So what does it mean? Every time we age, we don't have a discount in the price. We actually have an amplification of the
- price. The price goes up by a factor of 65. Right? If you take two to the six, you get 65. Anytime Bitcoin becomes two times holder, the pri and you can verify, everybody can verify. Go take
- the first year then go and look at year two. What is the difference between the price between one year one and year two?
- Almost 65. Then you take two and go to four. Check the price growth almost 65.
- It will change because we have this bubble. We have noise but roughly 65.
- This is the so it means you know that the price is going very very fast. At the same time, differently from what Sailor was talking about, the Bitcoin is like this uh bacteria that is doubling
- doubling and then when it arrives to half of the what is left it in the next move it covers everything and dies. With Bitcoin we are slowing down. This is why you see that curve
- like this in the type of graph where you have log and then linear index. uh while is a straight line so it is proportional in the log log chart. In the log log chart the straight line means that the
- scale of a price and the scale of a time are proportional to each other. So every time you have a change in time you're going to have a a proportional change in the scale of price and that means factor
- of 10. So if the first uh year we were going up f factor of 10 very quickly right within a year within a two years now as things progress everything slow down because now for example you need
- another change of 10 in time. So if if you go we go from days to weeks to months. So the next change of time of a price in in of a factor of 10 will
- happen in about eight years from now.
- >> Okay. So in in that scale we are going to have a change of price of 10. Uh so this is what the power law predicts that bitcoin will be close to a million dollar in eight years. But you see it took that is almost half of all the age
- of bitcoin when in the beginning >> we were going very fast. Now these are called diminishing returns. Right? So you can actually write an equation that tell us how right now for example yearly according to the power law we we are
- doing about close to 41%.
- >> Right >> by uh 20 years that is when actually bitcoin will be $10 million if we continue to follow the power law in 20 years that is the prediction um the
- returns will be close to 20%. So they are going down but now I say all the time because some people will say that is a bad thing right that we are actually having less returns but you know that allows for the system to
- adapt. So for example right now it's being adopted by institutions right so institution will not be interested in something that grows two times a year will be too unstable they want something much more stable right but as the system
- grows it continues to grow pretty fast but it slows down it allows for uh an optimization of a resources around it okay this why >> um and go ahead ask me a question and I
- can say more about >> well just to slow this down just a little bit. So, um it's we all are aware that there are laws in nature and they follow essentially mathematics and it's it's like a beautiful design, right? I
- mean, I I think it leads you to to wonder how >> how it was all engineered because it it's so perfect in its randomness. But you kind of say Bitcoin is not random.
- It follows laws just like a natural system.
- >> It follows the power law. You're differentiating between power law which kind of shows more stable growth over the long run as as opposed to exponential growth which might be fast fast fast but then ultimately dies
- something like I I I think of um >> I don't know the COVID pandemic right it was like fast and then boom it sort of fell off a cliff the power law I think I heard you describe before it it is similar to how cities grow correct right
- cities don't just all of a sudden fall off a cliff they continue to grow they might have issues and entropy and all that, but like they grow and and they develop and then at some point they reach a level where they're not growing
- that much faster anymore, right?
- >> Yeah. And actually this process it's always the same because when you plot it in so first of all if uh and this is also what uh these scientists that I mentioned Jeffrey West is actually in that beautiful book that I mentioned
- scales he has entire chapters about cities. So it take almost any important par parameter like GDP, the number of patents, uh the salaries in the city, how many libraries or gas station there
- are in a city, even how fast somebody works in a city. All these parameters are power laws. You plot it in a log log log, you are going to see a fuzzy power law because there is always some randomness, right? Because after all, we
- are human beings. We have some degree of freedom. But it's limited to this growth along this line. It's almost, you know, it's really amazing to see that graph and they have a graph um online that you can find look for power law cities where
- they have all these parameters all on top of each other all follow the same and it doesn't matter if you are in Australia, if you are in China, if you are US, Italy, they all follow the same power law. It goes something like uh
- whatever parameter to what determines that parameter the population to the power of 1 clause almost two 1.8 something like that. Um and it's
- universal. We use this term in physics universal when many things in different places in different situation follow similar patterns.
- It means okay these two things they could be the growth of animals and you know in terms of energy and cities they have the same power law they are in a sense the same phenomena right we make a connection because way they behave
- mathematically similar like a a sound wave is similar to a light wave right they have some things in common they have waves there are oscillations we have a period we have a frequency all these things for a physicist in a way
- all these things are the same thing.
- >> Yes. Okay.
- >> Um, yeah. Go ahead.
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- x-axis is the time, right? Whether it's measured in months or years and then the yaxis is the price.
- >> And so can you kind of crystallize again how you reach the 5.9ish and so and and what is the math again?
- So we started Bitcoin was worth nothing when it first came out and then it started to have a price in what 2011 or so?
- >> 10. Yeah.
- >> 2010. And then it grew and we hit 126,000 in October. Now we've crashed back down. So tell me those um tell me the power in in that.
- >> Yeah. So if you write the full formula is a price equal 10 to the -7. Uh it's this constant very small constant 10 - 17 means 0 16 zeros 1 and then the time
- you can me let's say we measure it in day. So today will be maybe we can check it out but 6,126 after January 3, 2009. We call it the genesis block, right? The time when
- Bitcoin was uh created. So we measure everything in terms of how much time is pass from the creation almost like a big bang right it was the big bang of Bitcoin. So you say how much time is pass then you take this number of days
- you take the power of 5.8 let's round it to 5.8 Right? And you get the price like if we did it today it will be close to 120 for example.
- >> So we should be at 120 right now.
- >> We should be 120. And then you say well but we are at 75. Yes because there are some oscillations around this long-term curve right. uh we sometime we are below sometime we are above but if you take the average like for example I can
- smooth that curve taking what is called the four-year moving average right I take I calculate every day is the average of the last four years the two curves are on on top of each other the
- the bubbles almost disappear they get smooted and you can see that this four years average approximates the power law almost perfectly it's a it's really incredible because there are we have some parameters to measure or how good
- the fit of this curve is is called one of these. There are many methods but one of the most classical is this quantity called the correlation coefficient that is a number between 0ero and one and for bitcoin for the bitcoin power law it's
- 0.97 last time I measured it means only 3% of the variation of bitcoin are not described by a power law otherwise in average the power law described 97% of
- the behavior of bitcoin >> wow in terms of price in terms of price now the beauty remember when I told you about the exponent because this I think is one of the crucial thing that many people miss uh that exponent it's a
- fingerprint of a phenomena for example just to give an historical example um one of the first power law that was uh discovered that in fact created almost like a the entire scientific revolution we started from there was the discovery
- of how planets move around the sun right the cop copernical revolution and then these scientists called Kepler He was fixated all his life that there was some kind of a hoarder, some kind of
- these planets were not moving randomly.
- There was some kind of law, right? To us seems obvious now because we know there is gravity or whatever. But at that time was a big revolution. Maybe we can find how God thinks, right? This how these people were thinking at the time. They
- were thinking the universe created by God and God does things in a particular matter, right? Starting with Galileo that says nature is a language written it's a book written with the language of
- mathematics is what Galileo said. So all these scientists in Renaissance were looking for patterns and Kepler found that if you take the log of the distance of a planet and the log of the time that
- it takes the planet to go around the sun it's a beautiful straight line. It's a power law >> and that power law is the power is two over three.
- >> Now at that time it was a mystery. Okay, there is this beautiful order that is so organized and differently from Bitcoin.
- These are really almost perfect points.
- It's really scary. You people can ask Jubet say hey make me a log log chart of a planet distance versus the period you know time that it goes around the sun and they are going to see this incredible beautiful perfect math right
- that the planets move with very precise mathematics and it was a big revolution of that time people were kind of shocked by this but it took almost 100 years to explain where it came from and it and
- and Newton did that Newton came down and brought this equation of motion you know force equal mass time acceleration and then he was able to explain that if it was a force an attractive force between
- the sun and the planet you could get this behavior this mathematical behavior well the same thing they did with this clever law that three quarter that they told you uh people explore it you know they don't stop there oh three quarter
- okay let's go and drink some beer right maybe they do that but after they think where this three quarter comes from and you don't if you're a scientist You are not going to sleep until you find the solution. You know this how we work and
- they found out in the book scale is explained very beautifully. It has to do with the distribution of vessels in our body because they are basically like network right they connect different part of the body that there is
- distribution of um food and energy to the cells etc. And that three quarter comes from the geometry in fact in fact the fractal geometry. You need to read the book to understand all the details
- but it's something about how the body organizes itself. It's this beautiful network and connection and this kind of gives us a clue of why the power law shows up in Bitcoin because one of the
- things that everybody says without ever going deeper is that Bitcoin is a network, right? You say, "Oh, it's a network. It's a network." Yes, networks show up as power a lot of the properties
- the number of connections how they grow the number of links you know how they connect with each other there are many studies that people have done on social network and they show that both the links so the number of connection and
- the nodes so the participants in the uh network grow as power loss >> and what happened with bitcoin I went and I look at all the other parameters because with bitcoin we have addresses
- We have a um the number of transactions, we have a ash rate, we have all these parameters >> and all of those are >> all of them are power laws.
- >> Wow.
- >> So what comes out? It comes out that this number six is a combination of two different power laws. One is the power law of the addresses. So if you do a plot and it's even more precise and
- beautiful, it's almost like a straight line. You take the addresses as a function of time and you take the log of the addresses versus the log of time and you get this power log with the cube with the t to the cube. So the number of
- address is equal to time to the cube.
- >> Wow.
- >> Guess what else grew exactly with this formula? Number of participants in this network.
- Power to the cube. Time to the cube.
- Guess which famous network grew like this?
- >> Facebook.
- >> The internet itself. The internet itself. In fact, I have a graph in my book where I superimpose wow >> the power law of Bitcoin of the addresses with the power law of the internet and they're almost on top of each other. Bitcoin is slightly faster
- than the internet by the way. Uh so what we are saying that uh addresses grew up with bitcoin not with this scurve because everybody say scurve scurve maybe you heard about that many
- technologies grow like an s-curve so they grow very fast actually curve is an exponential it's a double exponential grows up as an exponential fast then basically reaches the middle when almost
- every 50% of the population adopts that technology and then it slows down so it's an exponential but growing the opposite direction exponential. Bitcoin doesn't grow like that.
- >> They've used examples of that actually with other technologies like um appliances, refrigerators, the adoption an Scurve or phones or televisions. So those are exponential >> but these are not networks right? So if
- people buy a phone, buy a car, buy etc.
- But and maybe they are influenced by their neighbors but they don't show that powerful network property because look at this right we are here we are talking about Bitcoin we are we are going to a conference soon we are passionate about
- this topic we are evangelist etc it's the typical sign of a strong social network yeah and when these social networks manifest themselves they don't do it through this escort they do it
- through a power law and the beauty of a power law what is because there are always consequences Right. I'm trying to understand that this what the book is all about. We are trying to explain. By the way, this is my book, The Physics of
- Bitcoin. It just came out. It's >> like almost a textbook >> that covers all these topics and tries to explain it to people in a simple manner. But uh >> um you see the fact that we have a straight
- line, it means that the straight line is self similar. It's similar to itself at any point. You take a little section of a line, it looks like the entire line or it looks like another section of a line.
- Right? We call this property scaling variant. And in physics is very important because one of the quest of physics is to find what is similar and what is different. Right? If we find
- something that is self similar is very interesting because it means that it's almost like a holograph. Right? You can hologram. You can reproduce the entire picture of Bitcoin by just taking a
- section. And so you know when people say oh there be a time uh so they say something they have all kind of memes right one meme is uh um slow first and fast then right or later right or all
- all of a sudden something happens yeah and then suddenly well it's not going to happen with bitcoin if we follow the power law because all what the power law says is >> we are simply doing the same thing bitcoin is doing
- >> always gradual >> is always gradual and bitcoin continues to behave as itself. Whatever it was doing 12 years ago is doing it now but at a different scale. You see it's like a is reproducing itself at a bigger and
- bigger scale. Like an elephant is a scaled version of a mouse, right? We have the same physiology, the same cells. It's just that is bigger and in fact more efficient because it's using energy in a more efficient way. Same
- thing with Bitcoin. As Bitcoin scales up, it's still Bitcoin. It behaves like Bitcoin. It has the same description and equation that was described coin when he was two years old, but now it's
- a bigger scale of himself. It's like an elephant. So, it's more mature. It's a there are less variation. It's more stable. The heartbeat of an elephant, for example, is slower than that of a mouse, right? It's a more efficient
- system.
- >> Does power law apply to other assets like gold or popular stocks like um like Nvidia for example? Do they follow?
- >> In fact, one of the most popular graphic I ever posted was where I did this experiment. I took two random days, right? I'm taking two random days. I look at the price, the real price of Bitcoin and then I take the ratio of the
- price that is the change in the price and then the change in time. And you do this over and over again. You take the logarithm of both of them. And what you're going to see with Bitcoin that this beautiful fuzzy almost that looks
- like the power law of the cities that I described before this fuzzy power law starts to appear because we are not plotting the price as a power law. We are proing the changes in the price randomly, right? And they start to look
- if you go through the equation, you show it should look like a power law and it looks like this beautiful power law.
- Okay? Then you do it with gold. You do it with Nvidia. You go do it with SP500 and they don't look at all they look like S's like look something completely different almost like two different galaxies. They did it with you know kind
- of colorful dots and everybody got like thousands of likes because of that post.
- >> Why is that? I mean cuz they grow similar to Bitcoin and many properties.
- Why didn't it grow as a power law?
- >> Because they are not networks. All these things are not network. Like Bitcoin, we go to conferences, we talk with each other, the price is not determined by the market uh like in this kind of random way plus some drift. That drift
- that we see with the stocks like if you or gold right you look at uh SP 500 the last 25 years it looks is going up. In fact, you can fit a power an exponential to it. Okay, >> they are all exponentials and uh that
- exponential is mostly driven by inflation.
- >> Most of the gains that you had in the last 25 years by SP500 is nothing else but inflation. It's catching up with inflation. Basically, you don't gain anything. You are just barely beating inflation.
- >> Is inflation an exponential?
- >> Yes, absolutely. because uh roughly you can calculate a rate of growth of inflation and then it's kind of constant. It doesn't change much maybe grows a little bit but it does in
- roughly doesn't change and then you're going to have an exponential process because of that with Bitcoin we have this beautiful process that is the process that is chosen by nature uh and also things that kind of human construct
- that grow from the bottom up like for example a city right a city is organic people interact with each other yes there is some planning but uh it's not very stronger and in fact one of the
- things that you learn from the power law that you should not do much of central planning let things organize themsel and then the natural exchange of information and knowledge etc creates this process
- this is what happened with bitcoin it's a bottom up process that self-organizes and it chooses for whatever reason the path that nature likes like for example there is another article that I mention
- in the book and is a comprehensive article of it studies of the growth of teeth um horns shells um
- thorns in uh in plants all of them grow as power loss.
- >> Wow.
- >> So it's what nature likes. Now do you know what in nature some of the bad processes are exponential like cancer for example is an exponential. Now this guy this uh um um Jeffrey West in his u
- um there is a nice little talk that uh again I really suggest everybody to watch it's called you can google it is called the surprising math of cities and corporations and in this lecture right
- he introduces all these idea power laws he talks about the clay's law but one of his uh punch line in the end when he introduces the power law of cities he say he says cities are eternal. You take
- Rome, right? Rome has been existing for thousands of years, right? Uh they have n cities like uh Hiroshima and Nagazaki that are being nuked and now they are rebuilt and they are very thriving
- cities etc. It's very difficult to kill a city, right?
- >> And they all grow as power laws.
- >> But corporations are actually >> corporation is studied a corporation as an example and then they grow exponentially. And he says as a joke he >> there are no corporation that maybe there is only one exception that is the
- Vatican that is makes a joke that as a corporation right that has existed more than 150 years.
- >> Wow. Almost all of them die within 150 years because they grow as an exponential and then they don't have any other resources you know they run out of resources and they die their market is not is saturated by their products and
- they have some other competitor and they die >> but what does that mean for corporations that are backed by bitcoin essentially could they live forever strategy live >> exactly so this is one of the reason why
- I want sailor to start adopted this lang language of a power law because he could say exactly that. You say we are turning corporations into cities in these products that are bottom up products,
- you know, that are all based on the free interactions of people without any central government to tell them what to do. And these beautiful growth patterns that are organized, they are stable, they are resilient because there are a
- lot of things that properties are associated with power loss. Among them, they are very resilient. Again, this why biology likes this type of pattern versus others >> and Bitcoin is all these things to me is
- like something that every single Bitcoiner should talk about right we have the growth of Bitcoin in particular if we can show it scientifically that is one of the things I'm trying to do like for example right now I wrote an entire
- paper on these power law things that I'm sending to scientific journals because I want the feedback of a scientific community say well it's not some random analyst they came up with some crazy idea is actually a scientific fact that
- Bitcoin follows a power law. You know, this is one of the things and I even created you say I am the director of a scientific Bitcoin institute. I created this um nonprofit um at a certain point people can go online there are very big
- courses uh there be um scholarship that students can apply to because we are going to sponsor the scientific study of Bitcoin because our idea that Bitcoin beyond being an asset and all the things
- that we associated with Bitcoin is also a system is a system that is really interesting because it has application in economy has application in psychology in physics, thermodynamics, you know,
- with the mining, the use of energy.
- There are all these different issues associated with Bitcoin that are very cool to understand because you have millions of people coming together, interacting, doing something together, discovering what value means, right?
- >> A big section of a book, I'm trying to make a this case that maybe we have another a new way with Bitcoin to determine what value is. It's a scientific way. And if you think about a lot of uh valuable things in life are
- networks, right? We value city. We yeah cities are a very important reference, right? Most of the wealth comes from city. We live in city. We like the activity. You you live in Chicago, right? A big interesting city. Uh the
- brain is a network. There is one of the most valuable things as a human being.
- The body itself is a network. Life on earth is a network. All the most valuable things are network. And maybe by measuring the property of a network we can establish almost scientific way of what value is. So we can go from
- people say oh bitcoin doesn't have any value it doesn't support the business say no it's value come from this being this network that people created from scratch and is evolving and the interaction between people because
- literally the number of people the participant in the network determine the price because I I didn't finish the story of exponent right remember I told you the price is proportional to the six
- right and we say the address is draw with a cube. And guess what? If you do a graph of a price versus addresses, so basically measure how the price reacts when we change the number of addresses,
- it's a rough proxy for adoption. How many people adopt because you can say, yeah, well, some people have hundreds of addresses, some people have just few, but in average, you know, it's there is a proportionality between bitcoiners and
- number of addresses, right? And uh uh so we want to study how the price reacts when we change the number of people participating. So addresses let's say.
- So the question is if I double the number of addresses is the price doubling is the price tripling what it does? It does exactly this. If you double it, it goes four. If you triple
- it, it goes nine. So it's a power law with the square.
- >> And there is a name for this law that was discovered by this engineer. is called Met Calf Law >> and uh he wanted so he was the father of the internet uh you know the cable that connects you with the internet and uh he
- was selling these cables uh to university like at the beginning of the internet right when in the '9s so and many people didn't appreciate the value of this connectivity you know they didn't give it the correct value they
- thought well let's buy a couple of them so maybe we have a computer connected with a printer two computers connect with each other, maybe they can do something. They didn't realize the value of connecting things, right? And then he
- came up with this. They say, well, really what I'm selling to them is a very good deal because the price of these things is linear, right? You buy 10 and then you buy 100, you uh spend it
- 10 times more, right? But what is really the value of going from let's say 10 to 100 is not 10 times is 100 times because it's really the number of connection and he did a quick calculation and he was
- able to show if you have 10 computers and they are connected with each other the number of links is about 100 >> okay >> so the number of way you can connect this network >> okay >> 100 times and so he say wow this is cool
- because you spend 10 and you get back 100 right it's a very good value proposition. With Bitcoin, you have the same you have the same law. Every time we double the number of participant in the Bitcoin, the price goes up four.
- Every time we triple, the price goes up nine.
- >> So, it's very predictable. It's not it's not as random as we think.
- >> No.
- >> And when you combine these two, right, the growth of the addresses and this response to the addresses, guess what?
- You get something like this. The price is proportional to the number of Bitcoin squared. Let's say the growth of this bitcoin goes up bitcoiners goes with a cube. So if you take this is from m high
- school math. If you take the power of a power you multiply the exponent. So you have three times two that is six. And remember what I told you the price power law is time to six. And this where it
- comes from it comes from these other two power laws. one the how the addresses are growing in time and the other how price responds to adoption. If you combine them together, you get this power lo time. And it's really beautiful
- because it's a circle, right? In a sense, what they did is was what Newton did with Kepler's law. He found a more fundamental process >> that explain why the planets behave like
- they are.
- >> So, everyone is familiar with how volatile Bitcoin is, at least in the short term. And to your point, if you look at just a chart of Bitcoin's price, it's like up and down and up and down.
- And one of the things you can't predict is some of the aspects of our human psychology and behavior. These sort of black swan events, wars starting and everyone rushes and sells the thing that's most liquid, right? Or something,
- you know, geopolitical happens, a market crash, a banking crisis. Those are things that precipitate some of Bitcoin's crashes. But despite those things happening, you're saying it is still kind of tracked along this line
- where it hasn't it hasn't exceeded it or crashed too much to to basically go against >> most of the price is within what we call in statistics one sigma right so if you
- have a distribution of the changes uh like for example height right uh 65% so there will be an average height for let's say males in United States right and then The distribution will be like
- in this case is not a power law. It's what is called a bell curve. Right? So 65% of the data is within one sigma. Got it?
- >> Most of the data of Bitcoin is within this one sigma. But it's not very large.
- It's just a band around that power law.
- >> So and is actually kind of interesting think the values below the power law are much closer. In fact there is almost nothing beyond two sigma. you will expect you know there are some people
- because we say 65% they go >> you know beyond the one sigma right that are I don't know maybe the difference is 510 is the average sigma is 2 in so there are a lot of people that are still
- taller than six inches right less and less but uh there are some in this case with bitcoin we never go beyond one sigma and it almost creates like a floor okay >> and that sigma is about a kind of close
- to a value of 50%. So, >> so what's the sigma? What's the floor right now with >> the floor? We are kind of close to the floor. Uh, so right now should be around 56 57 that floor. Okay.
- >> And we think that floor comes from the cost of production of Bitcoin, right?
- Because now if you can you can do another power law. You can say, hey, what is the relationship between price and ash rate? It turns out that uh the um price is the square root of the ash rate.
- >> Oh, wow. that is you know the power of one over two. Uh so it's all power laws that is incredible. And if you do then a diagram of a price based on a rate you get that floor. That floor comes from
- this other power law.
- >> So we're supposed to be at 120. Where are we supposed to be? Let's say next year. Do you know?
- >> I think we close uh to almost like 150 if you go. Yeah. If we look at the middle line.
- >> Okay. Yeah. And you said in eight years a million dollars.
- >> A million dollar. And then in 20 years $10 million.
- >> How sure are you that that's going to happen.
- >> Okay. So you never be sure, right?
- Because if these were planets, we can say yes, right? In fact, they use that law to find they they didn't know planets beyond Saturn. You know, they didn't know Uranus, they didn't know Neptune. They use actually that to to
- find where the next planet was going to be, right? um and it exactly fell there.
- So with animals same like if we discover an animal that is bigger than elephant very likely it will be in that line that I describe right um because it will be a violation of fundamental laws with
- something like Bitcoin because we are still talking about markets we need to have a see to guarantee the growth of Bitcoin we need the capital right we need to have all these things happening >> but one I think if we if they do happen
- if we do investment if a bank continues to because we need big agents. People by themselves are not going to do it. We need to have to it's part actually of a prediction of a power law that as the system grows bigger and bigger agents
- are going to >> bigger pools of capital basically bigger pools of capital institutions of sovereigns as they come in um my bet you know because I call it a theory when you do a theory in science
- is basically you say look I think I it's different from what people think about theory right oh the in theory should be like that no in science is actually most precise as description of a phenomena.
- So I'm saying and it's predictive and say Bitcoin should be a power law it does grow as a power law it will continue to grow as a power law it's an you know it's a bet right when you do the like Einstein didn't know that the
- universe was going to behave according to his law then people did experiments and they verify right so these are very important part of doing science you need to have a way for people to disprove what you're saying right so if it
- doesn't follow the the law there'll be some problem it we will have to understand because So far it did follow.
- What happened for not following it?
- Right? An elephant will not grow its task as a power law because this what he does if he doesn't have food around, right? It will not have resources and so >> then it cannot produce. Maybe the power
- law of the growth is getting modified and change is actually almost a a tool for diagnosis that something is wrong with the elephant. So something will happen with Bitcoin if we don't follow the power law. Hopefully we continue,
- right? But power laws have been used in science as a predictive tools because with the elephant you can do the same.
- You can look where the elephant growth of a task is after 20 years and then you can extrapolate it to the next 30 years and you are pretty sure it's going to follow that line. So you can predict how big the task will be in 20 years, 30
- years. It's predictive because it has to do with mechanism. What is the mechanism behind the growth of this system? And the this system don't change all of a sudden the way they operate right now
- I you know if I had to put a number I would say close to 90% you know because I want still to leave some room for >> things to happen but what you were saying about the crashes um the crisis
- the war these are all temporary things >> you know it's almost like weather you
- the seasons continue to exist Even if uh weather locally can change right today we are supposed to have sun instead we had a rain but it's not going to change the nature of a growth right uh these
- are all oscillation in fact when we look at this parameter r square that says 97% is explained by the power law in a sense this is what we are saying that these oscillations sometime we have positive
- oscillations sometime we have negative oscillations but they kind of cancel each other right and they leave this overall path So, what should the average person listening take away from this? Um, because I'm sure you don't advocate
- trading of Bitcoin, right? And it it kind of tells us that we're very early.
- A lot of people think they're too late to Bitcoin, but even though there are these diminishing returns, >> it seems like it's just going to continue to go up from here, even if it's more gradual. Okay. So we have and pair if you know particular if you are a
- young person you know 20 years is not a lot of time and supposedly we are going up another factor of 100 in 20 years. So it's it's a big deal in particular because >> 100 times. So from here we're at 70
- something thousand times 100 >> 10 millions like we say 10 millions in 20 years close right close to 10 millions. Um and so 100 pair. So that is really cool. It's amazing particular
- because yeah, maybe it's not the Bitcoin in all it history so far went up 100 million times.
- >> The first transaction was like a $5 for 5,000 Bitcoin, something like that. So from that point to here we are 100 million, right? So it's unbelievable.
- Probably the only system in in all the history economical system that went up 100 million times in 15 years. It's unbelievable. Um, but it still has
- enough to go up 100 times by the time by the way the market cap of Bitcoin will be equivalent to almost all the real estate in the world. You know this is what we are talking about. Um and so
- that is an interesting fact but more fundamentally I will I would want to people to start to study this why they should read the book not because I want them to buy the book because it's really a act of love
- you know for the community I wrote this book because I want people to understand the beauty of Bitcoin it's a different angle right every you had a lot of ho guest that tell you a different angle of Bitcoin why Bitcoin is important why it
- is relevant interesting. But >> don't you think it's beautiful and amazing that we all love this system that is growing with the favorite growth pattern of nature, the growth pattern of
- uh biology, the growth pattern of galaxies, the growth pattern of cities, all these important system and and nobody told Bitcoin do this. It did it by itself. So to me if we explain it
- correctly in particular people like you that are very good in explaining things for the general person etc in a way that makes sense to people. It's a way of saying listen Bitcoin is so different from everything else because all these
- are bad exponential associated with cancer companies they die and Bitcoin is like a city you know Bitcoin is like tooth and nails and thorns and shells you know these natural forms to me this
- if you can simplify this message >> and because it's not a poetry it's science actually it's based on data and the science to me is like one of the most convincing
- orange peeling argument that you can make right to people that no it's not this it's like when people say speculation absolutely not speculation will not grow usually speculation like bubbles and other things like that they
- grow exponentially the opposite of a power law power law is self-regulating right is slowing down of things there is something deeper there is a network quality of a system u and you know okay
- everything else is different from uh Bitcoin because it's not speculation because it would not grow as an exponential is not a pyramid scheme because also that grow as exponential all the things that it does have value
- because it's finding value not by people imposing it from outside but it finds it by itself by growing through adoption you know so it's I think it's beautiful once you understand it there are a lot
- of consequences yeah >> we are adding a very important story to what Bitcoin You know, Bitcoin follows the laws of nature. Amazing.
- >> Okay, so just going back to the very beginning, if you could summarize power law in one sentence again, like you're talking to high schoolers like power, what is power law and what does it mean
- in one sentence?
- >> It's the a nonlinear relationship between two quantities, right? So you change one quantity, let's say the temperature of an object, and you're getting something much more out of it, right? because you're taking the power.
- So I double the temperature of a light bulb. I don't get two times the light. I get it 32 times >> because of that four, you know. So it's a non what we call a nonlinear
- relationship. It's a um and you can go in both direction for the animals because that value is below one there is a discount.
- >> Same thing with um cities. If you look at much space a city um um occupies versus the population is similar to that clever law there is a discount. Why?
- Because people start to build skyscrapers etc. they utilize space in an efficient way. But if you look at all the positive things with cities that number is above one. So you get actually an amplification and with Bitcoin we get
- an amplification of the price because of that square right the metal law every time we double the population of Bitcoiners we get four times the price um and uh and the growth itself is a
- power law that means actually it's growing faster very fast with the cube you know and when and with the with the price every time we double the age of bitcoin we at 65 because of that six uh
- so it's It's similar to how city grows, all the good things about cities, how they grow. So, >> it's really fascinating. I think this will make a lot of people that have been frustrated at the bare market happy and
- looking forward to when um when Bitcoin resumes its climb towards 1 million and 10 million. So, Giovanni, it's been great to chat with you. Where can people find your work?
- >> I am on X. Um I don't know if you can link it to the video. uh and u um I'm I have a YouTube channel that people also can find but okay yeah most of the time I am on X so people can DM me interact
- with me and u I'm going to actually there is a book associated with the physics of sorry a website associated with the physics of bitcoin okay >> uh and people can go there it's called the physics of bitcoin.com
- >> and is this out yet or no >> it's out yes yes in Kindle and uh the printed version will be around 18th.
- >> Okay.
- >> Um I can have a people sign.
- >> All right. I'm I'm going to be signing mine. So maybe read mine first. You might need an introduction and then read that one. That one's This is more of an appetizer book. This is more of a main course.
- >> Exactly.
- >> Giovanni, thank you so so much. Um it's great to chat with you. Thanks for joining me in person. And how come there aren't more Bitcoiners in Italy?
- >> I know. We need to do something about that.
- >> I'm waiting for a Bitcoin conference in Italy. Like a really good one. the the institute actually is going to have his headquarter in Italy in this hub. There is a uh there is a company uh that is actually sponsoring a lot of projects in
- Europe and they are building this hub in Torino. It's a fourtory building with the first floor on this main square in Italy. Uh so you should actually come and visit.
- >> I should I should and the institute will have an office there. So being Italian for me I was there recently and I was pretty sad of the state of uh Bitcoin there. Many people are very interested
- but uh it's there is something stopping you know the culture or maybe even the politics and so we will try to do something about >> yeah I would love to see some circular economies in like the Amalfi coast tuskanyany I'm waiting for it. So
- Javanni grati mle thanks for joining me >> thank you so much for checking out this episode of coin stories. Make sure you're subscribed to the show so you don't miss any new episodes. If you can, turn on those notifications and leave us
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- please feel free to reach my team at info@talking bitcoin.com.