Source: Question 3

Why BTC is not a common asset, but more like a natural phenomenon governed by a universal power law, because the system has recursive, infinite feedback loops.

BTC power law is not just a model, but a powerful theory about the nature and behavior of BTC.

BTC power law was initially an empirical observation of the price pattern of BTC. But it is now evolving into a coherent and powerful theory of BTC behavior. Recently, we found that Hash Rate, Address, Transactions, and Price are all power laws of each other (as we already knew from previous work), and also power laws of time.

This is incredible because it indicates that the evolution of Bitcoin is driven by the property of invariance of scale. It also perfectly aligns with the actual meaning of Bitcoin: a self-referential and self-adaptive network. In particular, Difficulty Retargeting, one of Satoshi Nakamoto’s most brilliant innovations, is the key mechanism behind the power law, rather than scarcity. This constitutes the adaptive property of Bitcoin. The power law is a mathematical and physical expression of an iterative process where the output becomes the input (due to Difficulty Retargeting, Hash Rate now affects future Hash Rate). As I have demonstrated, this is not just in words, but also demonstrates precise mathematics, which gives rise to the observed temporal power law.

Therefore, although it didn’t have causality before the BTC power law, it is now more complete and powerful than any competing model. In fact, we can now explain why we see such strong barriers at the bottom (this is due to Miner Capitulation and perfectly reproduced by the iterative model of BTC), we can explain the depeg of Address and price with Hash Rate during the Bull Market (Hash Rate will not follow the frenzy during the Bull Market because it takes time to invest millions of dollars in infrastructure and new chip technology to catch up), and so on. Almost all aspects of BTC behavior can be explained by the power law theory of BTC behavior, it is powerful.

BTC Timely Discovery of Power Law

I usually don’t include these early transactions because most early adopters exchanged BTC for pizza. However, when you include them (adding the earliest known US BTC transaction to the dataset, which is very close to the trend), there is almost no difference between the current slope and the slope of all data, which confirms the goodness of the model. The dashed line is the current model, and the red line includes the earliest transactions.

Power laws are everywhere!

I previously mentioned the power law known as Kleiber’s law. It determines the relationship between the body weight of an animal and the energy it needs to survive. The scale ranges from small creatures like fruit flies to elephants, spanning 7 orders of magnitude. This is essentially what BTC went through when trading 10,000 BTC = 1 USD.

Scale immutability

Let me give you an example of another research area I’m involved in (besides astrophysics), namely sleep neuroscience. Especially the brain waves during sleep. I know this sounds unrelated, but let me explain and you’ll understand.

I specialize in understanding a sleep stage called slow-wave sleep. In this stage, we have large and slow brain waves (about 30 per second compared to waking EEG, and slow waves at 1 per second), which are considered a sign of Depth sleep. The larger the waves, the deeper the sleep. Therefore, when you are undergoing sleep studies in a clinic, it is important to calculate them or use them to determine someone’s sleep status. In my work, I have to try to understand this phenomenon. Given my training as a physicist, I entered this field as a Newbie, but this sometimes helps to ask questions that insiders in this field typically do not ask. For example, the manual that sleep doctors use to identify these waves says that only very large waves above a specific threshold are considered slow waves. If they are smaller than this threshold, smaller waves with similar features (such as their frequency) are not considered slow waves.

Having an arbitrary threshold sounds absurd, so I conducted a study, collecting all waves with such characteristics (such as their frequency range, shape, and other common features, excluding size). What I found is: they are scale-invariant! Even no one knows. There are large and small slow waves, and doctors tend to focus on the large waves that are easily visible to the naked eye, without really delving into this phenomenon.

Most doctors don’t know about the scale of immutability and its correlation. These large waves are the limits of the range and do not represent the phenomenon at all. They are large rare events at the tail. The distribution of these waves has a very long tail, and these events are located at the very end of the tail. Most slow waves (thousands) are much smaller, and there is no artificial threshold to distinguish their size. It is only randomly determined by some doctors in the past to decide how big the slow wave should be. But that’s not how the brain works. All of these slow waves are important. Perhaps for young, healthy subjects, large waves can serve as a measure of good sleep, but for elderly patients (whose waves decrease with age and are correlated with cognitive decline), it is a very bad measure that may lead to some diagnostic issues.

I have proven this in my research. You can publish a paper and get some praise from other researchers, but in the field of applied medicine, no one cares and they don’t change their medical research methods. This is a very sad part of medical research. Anyway, what does it have to do with BTC?

ETFs are big slow waves. We notice them because they are large, they are at the end of the distribution, and our human attention is drawn to them. But BTC has gone through many such events, large and small, such as when the network was small and few more people joined, the first website to talk about BTC, the first media to discuss it, etc. There are proportionate events at any point. We don’t remember them because they are small and all other slow wave doctors will ignore them. If my finding that BTC is a scale-invariant system is correct, then ETFs are the events that BTC needs to take the next step in its development. Nothing has changed. I know some people think this is Unfavourable Information. It is not. ETFs seem to affect current prices and may amplify the bull run that appears after the Halving.

The peak of the cycle may be larger than we expected, rather than declining as in the past, it may be as large as some early peaks. But these are only “local” effects (they involve changes at the moment), not long-term trajectories. As I have said many times, the fact that BTC follows a power law is a sign of health and strength, and we hope to support this. But in terms of understanding the scale immutability of BTC, they will not change the long-term trajectory of BTC, as there is no evidence that ETFs are different from all other events from a scale perspective. Perhaps I need to delve deeper into this and prove that the inflow of funds into BTC has some kind of double logarithmic relationship with BTC price, and show that it has scale immutability like the price itself, but currently this is my intuition and understanding of the scale-invariant system.

rise and power-law spiral

The Fibonacci spiral is related to the power law spiral, they are similar but not exactly the same. There are many rise processes that follow the power law spiral instead of the Fibonacci rule. For example, the growth of animal teeth and horns, or tree rings.

BTC, a complex dance of power laws

BTC is a Depth network full of power laws, which can be seen everywhere:

Price, Hash Rate, Address, and volume are all power-law relationships, and they also follow power-law distribution over time. Even the holding time and wealth distribution follow power-law distribution (the latter is power-law distribution, which is essentially slightly different from other distributions).

But volume pump with prices. They are also related to power laws. What is happening is a self-regulating process. It takes higher and higher prices to change the number of transactions by 10 times. Power laws are sometimes not intuitive, but if you don’t understand BTC, you can’t understand BTC literally. Every BTC enthusiast should keep up and try to understand how power laws work. Higher prices lead to more transactions, so in a sense, there are more BTC available on the open market. This may seem contradictory, but the premise is that you don’t understand power laws or use them to understand BTC. Please note that transactions are in BTC, not USD, so not only more USD is traded, but also the quantity of BTC.

The virtuous cycle of Proof of Work

The mathematics of the iterative process is the mathematics of power laws.

The power law is the result of an iterative process, and we can prove this: dPrice/dt=5.82 * price/time. Super cool! You can iterate this formula into the future, but of course, as you add more future points, it tends to a general power-law trend. So, it’s best to tell us the price 1-2 days in advance. Basically, you can create charts with different weights, which contribute to the price. The spot bundling price itself seems to give a good estimate of the current price, not a trend price, but the current price (a bit conservative during the bubble period, but still responsive to them). hash seems to indicate where the bottom is. Solving the problem between the two.

Maybe most of you have never studied higher calculus or any calculus (or hate it) at all. But for those who have or want to learn a little here, why power laws are the result of iteration. Let me show you the math (it’s a bit long, but I assure you it’s worth it if you have the patience to read it all): Let’s consider the equation in the form of dy/dt=n y/t. This is an equation called a differential equation. It is used in mathematics and physics to represent the change of some quantity. For example, if I want to represent the change of an object’s distance on y as a function of constant acceleration a, I can write it as dy/dt=a t, where dy/dt represents the change in distance with respect to time. Here, I’m simply saying that the change in distance is directly proportional to acceleration and time. It is one of the simplest differential equations. Solving the equation means finding a y equation that satisfies the equation (meaning the right and left sides are equal). Once you find such a y, you know how distance changes with time. There are many methods to solve differential equations. But one of my best professors told me (I still remember how surprised and confused I was when I heard this, but it’s the wisest mathematical advice ever) to guess a seemingly meaningful solution and test if it works. Simple! So what is a good guess for this equation? Well, on the left side, we have a derivative, and the derivative of t² is 2t, so I propose as a solution the form y=1/2 a t², so the 2 gets canceled out in the derivative, and both sides have a. You can check if this solution satisfies the equation: On the left side, dy/dt=d(1/2a t²)dt=1/2 a 2t=a t, which is equal to the right side = a t. So y=1/2 a t² is my solution, and interestingly, distance increases with the square of time.

Note: For a calculus expert, considering the nature of derivatives, this is certainly an easy guess, but I am trying to illustrate a point. Well, let’s go back to the original equation we want to study. dy/dt=n y/t. Please note that this equation is very peculiar because the quantity we want to solve for is also on the right side, so basically the change in this quantity depends on the quantity itself! Or in other words, the output of the equation is also a part of the input. That’s why I use it as one of the simplest examples of an iterative or feedback loop process. Let’s make a good guess about the solution to the above equation, y=A t^n, right? Where A is just a constant, it’s not that important. Let’s substitute: Left side: dy/dt=d(At^n)=A n t^(n-1), right side: n y/t = n A t^n /t=An t^(n-1). Left side = right side. Solved! But what is y=A t^n? That’s a power law! For BTC, it’s Price=At⁵.⁸², or for Hash=B t¹¹.⁴, or Price=CHash¹/², and so on. All power laws or iterative processes (output = new input). So now you can add the change dy/dt to y, and you get a new y, which can be used to solve the change in y, and so on. Therefore, power laws are the result of feedback loops, which we know exist due to the interaction of Miners and users in the network. That’s why Hash Rate, Address, and prices themselves are all power laws of each other, as well as power laws of time. Therefore, value, energy, time, and the power law adopted. How cool is that???

The reason we see such a strong and consistent barrier at the bottom is because of the ‘Miner Capitulation’ after the burst of the bubble. This is the bottom line where miners lose money through mining. The system cannot survive.

BTC: A Vital Network

As an organism of the network

City and Social Web

Unstoppable Time Machine

Scarcity is not the reason for driving the price of BTC

This is a very short-sighted concept of economic activities. The entire operation of modern society is based on improving productivity through scientific and technological advancements, overcoming these limitations. For example, famine is now more of a political problem rather than a resource problem. If we truly want to, we have the resources to overcome hunger in the world. The fixed supply of BTC is more about not diluting the ‘stakeholders’ and thus creating false scarcity. This is a very different attribute, more important than scarcity. Malthusian scarcity theory: This theory states that the supply of food cannot keep up with the rising population, inevitably leading to disease, famine, war, and disaster.

The guy who told me she used the scarcity argument to tell people to hurry up and get some BTC (which is good news, by the way) also told me to “stick to the numbers”. I followed her advice (not sure exactly what she meant, but again I knew her intentions were good). But math is math. There are two models here, the power-law model has zero assumptions about scarcity and is based only on the observation that the price is pumped in a predictable way. Scarcity is not part of the model at all. The other is S2F, where scarcity is the main driver, in fact, it assumes that scarcity increases over time. The power law (not assuming scarcity) leads to “hurry up and buy some BTC now”. As you can see, S2F means that you can join at any time and still get the same amount of earnings, whether you joined 10 years ago (again held for 4 years) or after 10 years (again held for 4 years). SAME HODLING TIME). During this period, both investors will receive a 10x return. When you notice a power-law model, it’s important to join as soon as possible. So, do you see how people use scarcity arguments to come to illogical conclusions that are not supported by facts?

I will publish this article and then spend some time following other content, because this topic is not so popular for many people. But this is very important, and I think I am doing it right when most people are confused about it (which is very surprising to me, because it seems that almost everyone has got it wrong). Paper: Only scarcity is needed as a security tool to prevent counterfeiting in the monetary system. BTC does not need scarcity, because it can already prevent counterfeiting (with one exception). Note: This discussion revolves around the “monetary system”, so it does not apply to investments, philately, or other valuable things or activities. Only the monetary system, so please focus the discussion on this point. Let’s use 4 examples to explain this point.

This article is a bit long, but I think it’s worth reading because it will clarify a very important misunderstanding.

1. Casino: A casino can be understood as a currency system. Customers come in and exchange some ‘valuable’ things (such as US dollars), and they will get some chips. The chips are exchanged at a precise Exchange Rate, with red worth 10, blue worth 50, and yellow worth 100. The Tokens are made of cheap plastic, so they are not related to the scarcity of the materials used. They are not as valuable as gold. But they are difficult to counterfeit, because no one will make more of these chips in the bathroom. They perfectly fulfill the functions of currency. They are not even a fixed Token system, because as more and more customers come in, the cashier will give away more Tokens, but these additional Tokens will not dilute everyone else’s Tokens. Their value is fixed at the entrance and will not change during the night when customers are playing. But the system operates well as a currency system because it has clear transaction rules, it is linked to valuable things outside the system, and no one counterfeits Tokens. In such a system, the role of scarcity is zero.

2. Monopoly game. Similar arguments. The whole game should simulate a competitive economy, even in a very simple way, where there are winners and losers. There are some very cheap tokens (which we even use as memes for worthless money), but they are meaningful and worthwhile in the game. The supply is limited, but it actually increases as players move on the board and earn game currency rewards in proportion to their luck and/or gaming ability. No one counterfeits money (cheaters can take money from another game, stuff it in their pockets, and then pump it out in the game when no one is watching, but this is not a fun way to play and it may be easily noticed by other players). The system is closed; there is no money coming in or out of the system except through fair game rules that everyone understands and agrees on. Therefore, scarcity is not required, nor is fixed supply.

3. Ideal, non-existent, but possible in people’s imagination, a society where there is no lying or deceiving. These aliens (of course not human) never lie or deceive, their brains are not like that. I know it’s hard to imagine, but please play along with me. The system may not be closed, it can interact with other systems in this imaginary world (where there are different countries and peoples, but all are super fair and respect rules and laws). In this case, people can use anything durable as currency. All you have to do is use some recognizable symbols to mark ‘money’ to indicate that it is money, or use some identifiable shapes or colors. Colored coded stones with paint that won’t chip off, or stones with special markings made by certain central authorities, or anything durable that can be used as currency. There is no need for scarcity, because counterfeiting also does not exist. You can also track this money by having stores and similar banks track the total supply, and when coins are lost or damaged due to wear, other coins can be provided in a fair and consistent manner. In this crazy world, even the government is fair and honest (well, I know I’m stretching it), so they wouldn’t do anything equivalent to printing money (except for the alternative of replacing lost or damaged coins and maintaining a stable supply as I mentioned).

4. The Roman Empire used gold and silver coins, which was an open system. The issuance of the Roman Empire was made of precious metals and represented units of higher value, made of a rare, durable metal called gold. The government stamped and guaranteed (at least initially) the purity of the metal on the coins, and each coin had its weight value (which means that even if you melted it down, you could get the value of the metal on the open market). Choosing these two metals, especially the more valuable one, was because they were “scare” (relative to other metals or even other valuable things). Considering the above example, there is only one reason for doing so. Reduce and/or avoid (which is basically impossible in the real world) counterfeiting. Because gold is hard to mine (in fact, mining technology had reached its limit in Roman times), bad actors find it difficult to obtain some gold and mix it with other cheaper and rarer metals to create more coins. People can melt existing coins and then dilute them (by the way, this happens frequently, especially in the peripheral areas of the empire), but the coins still need to contain a significant amount of gold to pass as gold coins (in terms of weight and other typical characteristics of gold), so this counterfeiting process is at least constrained by the fact that the materials used for currency are scarce and valuable. But as you can see, the choice of such materials is entirely based on security issues, not on giving money itself value. In a society where everyone is honest, all that is needed is some fixed supply, or even an unfixed supply, with simple and clear exchange rules that are fair and agreed upon by everyone.

So what about BTC? BTC solves all this in the following ways: 1) A fixed, unchangeable total supply. Because it is a digital technology, this is the first time in human history that this has been achieved. The algorithm behind BTC ensures that this supply cannot be changed unless the entire system reaches consensus, which is difficult to achieve in any case. 2) Before the total fixed supply is reached, the supply is gradually increased through a very precise, understandable agreement (by participating in the system, you implicitly agree to its rules), using a transparent method supported by security measures equivalent to ‘scarcity’, which is the energy and work exchange of hashpower or obtaining coins through mining. You won’t get anything for free, but you can exchange BTC rewards for something valuable (energy). This is equivalent to buying chips with dollars at a casino, exchanging ‘valuable’ things for another. This is another security measure to prevent counterfeiting and the only place where the concept of scarcity is reflected (although people can use abundant solar energy to mine coins, so it is not true scarcity itself, but rather the conversion of one form of energy into another form).

When we talk about BTC, the issue seems a bit remote. The number of coins, their divisibility, and the fact of fixed supply are irrelevant to scarcity itself. All of this is related to the clear rules of the system and based on Consensus. The fact that the total supply is fixed is a means of reaching Consensus (through previous laws or rules) around the issue of total currency supply (which may be a stumbling block in any other currency system, in which the central authorities or democratic procedures determine the supply regularly). Over time, the total supply and supply output are chosen by the system itself at the beginning. That’s it. These rules make things simpler, which is why it’s so brilliant. I hope my example can clarify why scarcity is a bad concept when it comes to the idea of ​​giving BTC value. I believe this will cause confusion in the community, and it will be even more confusing when we try to explain what BTC is to others. I won’t insist on this anymore, at least not now, haha, let people think and see if this is a useful way of reasoning. Thank you for listening.

BTC is the pizza that can nourish the whole world (please believe the words of the Italian). Do you know that fund manager lady (not sure about her name, it doesn’t matter) who had a big meltdown and said some ‘obviously’ stupid things that diluted the value of BTC for many satellites? Of course, she said some stupid things and the internet went crazy, making fun of her for days. But the reason she said that is because the emphasis on scarcity confused people, especially non-BTC people (and BTC people). Although the BTC people who follow her are not wrong, they are also not right. From a logical and mathematical perspective, they are correct, but from a narrative and educational perspective, they are wrong. One of the favorite examples people use to prove her wrong is that you cannot solve world hunger by cutting a pizza billions of times. But you know what? With BTC, you can. In fact, that’s exactly what we’re working on.

We hope BTC becomes the world currency system, so in a sense, it’s like providing nourishment (or serving some function) for the whole world. We emphasize the wrong concept. That’s why I insist that scarcity is the wrong perspective and narrative for BTC, at the cost of creating some friction and defending an unpopular idea. We missed a huge opportunity to point out that yes, there is a way to nourish the world with 1 pizza, by making the pizza very, very, very nutritious, where 1 small slice is very nutritious and can meet the needs of everyone on earth.

If BTC is destined to become the world’s monetary system, then it needs to be the magical pizza we talked about, which is impossible. We are just lifting stones to smash our feet by following scarcity, which makes our view of the value of BTC (and why it is so unique and important) wrong compared to those outside the community. Let’s start thinking about BTC from the perspective of abundance and infinite utility, rather than scarcity. BTC solves all of these problems, even the world’s desire for a fair and just monetary system.

S2F Model

Other measures of BTC scarcity

Power Law Life Course

I use the term “model” in BTC to represent power law, to curb its importance and carefully consider its meaning. But it’s not the “model” in most people’s perception of a mathematical model. If it is true, and I say if, then it tells us bigger things about BTC. It is a fundamental property of the system. This means:

1. Scale invariance. immutability.

2. Sustainability.

3. Adaptability.

4. Order and organization.

5. Predictability.

6. Intelligence and information.

7. BTC is like a city and a living organism.BTC就像一座城市和一个活生生的有机体。

8. Long lasting and resilient.

9. Good things come in time.

10. Unavoidability of 1 M and even 10 M BTC.1 M and even 10 M BTC’s inevitability.

BTC will do what BTC will do. We are all humble observers of this amazing phenomenon. However, if my discoveries even come close to the truth, then you would want BTC to have these attributes, mathematics tells us that they are not wishful thinking, but rather its mathematical and scientific truth.

When we talk about the value of BTC, one thing to consider is that human productivity and capacity are rising at an exponential rate (while the value of BTC is rising at a power law rate). The goal of BTC is to capture an increasing amount of human productivity value and ultimately represent the entire monetary system (with continuously rising value). Given the limited supply and the rise in human productivity, the value will continue to rise. The upper limit is not meant to dilute or allow any arbitrary force to capture the majority of this value through arbitrary dilution. But this is not scarcity, on the contrary.