Can We Consider Bitcoin as A Physical System Given It is a Power Law?

The opinion piece by business analyst Adrian Morris, published on Cointelegraph

https://cointelegraph.com/news/time-to-ditch-bitcoin-power-law-theory,

misinterprets several key aspects of both the power law framework and Bitcoin’s behavior as a system in his critique of the Bitcoin Power Law Theory (BPLT). Unfortunately, the article garnered more attention than it deserved, given the lack of substance in its arguments. While the BPLT remains the most robust framework we currently have for understanding Bitcoin’s behavior, there are numerous misconceptions and misunderstandings surrounding it that need to be addressed.

I want to clarify these points, correct misconceptions, and provide a more detailed response to the arguments presented.

Preface
To learn more about the Power Law Theory please read my main article on the theory here:

https://giovannisantostasi.medium.com/the-bitcoin-power-law-theory-962dfaf99ee9

Also, this is a useful website site for an introduction to the main concepts (power laws, scale invariance, and Santostasi’s Iteration).

https://bitcoin.powerlaw.live/

The Bitcoin Power Law Theory (BPLT) is grounded in indisputable empirical observations that have been rigorously examined over time. The theory’s validity has been verified using several mathematical and statistical tools, and its conclusions have been confirmed by numerous professionals (besides my 12 years of work on the subject) with extensive experience in scientific and data analysis. Among those who have endorsed the BPLT are F. Krueger @dotkrueger, a mathematics PhD who worked as a quant for several years on Wall Street, and S. Perenot, @moneyordebt, an Astrophysics Harvard PhD, who independently rediscovered the power law in Bitcoin after my original work.

Additionally, Sina @Sina_21st, a professor of Finance and CEO of a financial consulting firm, and Gerald Melino @BTCGoldChart, an engineer and statistician with years of experience in quality control, have carefully reviewed the mathematics behind the power law and found it to be a valid interpretation of Bitcoin’s behavior over the long term. These experts, along with several other engineers and scientists, have independently confirmed the strength of the power law model, reinforcing that it is not merely a theoretical construct but a reliable framework based on observable trends in Bitcoin’s long-term growth. In addition, I’m the process of writing a series of scientific articles on the theory to be submitted to the appropriate peer-review journals that will help us to create interest and consensus in the scientific community on Bitcoin as a valid scientific topic.

Before addressing Morris’s criticisms, it’s important to clarify that none of the validation tests supporting the BPLT rely on the assumption that Bitcoin is a physical system. This assumption is not necessary to conclude that Bitcoin follows precise and predictable mathematical patterns. In fact, this misunderstanding undermines much of Morris’s critique, as it incorrectly frames the assumption of Bitcoin being a physical system as the foundation of the BPLT. On the contrary, it is a conclusion or a philosophical perspective, that complements the theory, not its starting point.

Mathematics stands on its own; even without prior knowledge of the specific data in question, we could have reached the same conclusions about Bitcoin’s behavior based purely on mathematical analysis. The patterns revealed through the power law framework are independent of any assumptions about the nature of the system itself. This by itself could be all what is needed to say to respond to Morris’s article given that is basically a repetition of this unfounded thesis over and over again.

However, since many of Morris’s claims are frequently raised on social media and by other skeptics who haven’t taken the time to thoroughly explore the theory, I will take the opportunity to address them point by point. My goal is to inform readers about the relevant topics and demonstrate how the Bitcoin Power Law Theory not only holds up under scrutiny but also reveals fascinating implications and far-reaching consequences.

1. Misclassification of Bitcoin as a “Physical System”

The article asserts that classifying Bitcoin as a physical system is a “category error” and that Bitcoin’s nature as a digital asset makes it more appropriate to model using information theory rather than physics-based models like power laws. This is a fundamental misunderstanding of the theory.

The Bitcoin Power Law Theory (BPLT) does not suggest literally that Bitcoin is physically like a planet or an atom. Instead, it emphasizes that Bitcoin exhibits power law behavior, which is often found but not limited to physical systems. Power laws emerge in complex systems — social, economic, and even technological systems — where feedback loops are present. In fact, power laws have been widely observed in phenomena ranging from city growth to income distribution and even terrorist attacks, as demonstrated in the works of Geoffrey West and Sean Gourley.
A great book to read on this topic is:
https://www.amazon.com/Scale-Universal-Innovation-Sustainability-Organisms/dp/1594205582

Bitcoin, with its decentralized and evolving ecosystem, behaves as a self-regulating system, with price, hash rate, and adoption reinforcing each other through feedback loops. These feedback loops are mathematically modeled by power laws because they are iterative and interdependent, as described in my theory.

2. Human Dependency and the Social Aspect of Bitcoin

The critic argues that Bitcoin is influenced by human behavior and subject to global social and regulatory pressures, thus suggesting that it cannot be modeled by a system like the Power Law Theory. While Bitcoin is indeed influenced by external forces, the power law model remains robust because it reflects long-term trends, despite these short-term fluctuations.

Every economic system — including fiat currency systems, stock markets, and cities — exists within social and political contexts and they do experience behaviors that can be characterized mathematically both in the short and long term.

But Bitcoin in particular is subject to feedback loops that are generative of power laws because it has several interconnected feedback loops at the core of its nature.

The article misunderstands that power law models do not claim to predict short-term anomalies like regulatory changes or social pressures, but rather focus on the system’s long-term scalability and stability. In Bitcoin’s case, its infrastructure — hash rate, mining difficulty, user adoption — all show scale-invariant properties that fit into the power law framework.

3. Misunderstanding of “Scale”

The use of the term “scale” by Morris is vague and not in line with its scientific definition. In the context of the Bitcoin Power Law Theory, scale invariance is a key property. This means that as Bitcoin’s ecosystem grows, its behavior remains proportional, allowing for predictions to be made across different scales (orders of magnitude).

Scale invariance has been observed over 9 orders of magnitude in Bitcoin’s price movement, and as I have demonstrated, it is likely to continue for another 1 or 2 orders of magnitude (over the next decade or more). The article claims that Bitcoin’s “social, political, and economic” nature makes this impossible, but this misses the core principle of scale invariance. Systems governed by power laws are not limited to physical objects; they apply wherever self-similar, iterative processes are at work — Bitcoin’s adoption, price, and hash rate exhibit this across time and user growth.

4. Bitcoin’s Feedback Loops

The article completely overlooks one of the most important aspects of the BPLT: the feedback loops that tie together Bitcoin’s price, hash rate, and user adoption. These loops are central to understanding Bitcoin’s growth and stability over time.

• As the price rises, mining becomes more profitable.
• Increased mining leads to a higher hash rate and greater network security.
• Greater security attracts more users, which increases adoption and demand for Bitcoin.
• As user demand increases, so does the price.

This process has been named the Santostasi’s iteration and it is described here in detail:

https://bitcoin.powerlaw.live/readme/santostasis-iteration

These feedback loops create a self-reinforcing cycle, which is well-captured by power law dynamics. The critique fails to account for this essential feature of Bitcoin’s behavior, instead attempting to dismiss the power law as inappropriate without addressing the evidence that supports these relationships.

5. Predictions and Falsifiability

The critic’s concern over the BPLT’s predictive ability is unwarranted. At the core of the theory is the idea of Scale Invariance:

https://bitcoin.powerlaw.live/readme/scale-invariance

The Bitcoin Power Law Theory is scientifically robust because it is falsifiable. The theory makes clear, testable predictions about Bitcoin’s future behavior based on the observed Scale Invariance properties of the system, which can be evaluated as more data becomes available. For example, it predicts that Bitcoin’s price will follow a path toward $1 million by 2036.

While short-term price fluctuations can occur due to external factors (e.g., regulatory action, market speculation), the long-term trend described by the power law model has proven remarkably accurate over the past 12 years. The critic does not present any concrete data or counterexamples to disprove this.

6. Bitcoin’s Unique Hybrid Nature: A Social and Physical System

While the critique attempts to dismiss the idea of Bitcoin being modeled as a physical system, it overlooks the fact that Bitcoin is an inherently unique hybrid system. Bitcoin is not just another asset but a complex network with both social and physical dimensions. As I’ve demonstrated in my original article, all of Bitcoin’s on-chain parameters — including hash rate, price, and user adoption — are interconnected by power laws, forming a coherent and predictable system. This is not a superficial observation; it is a deep, empirically supported finding that has persisted for over 15 years across multiple orders of magnitude.

The critic also misunderstands the broader context of power laws. While power laws are observed in many fields — from physics to social networks — they are particularly relevant to Bitcoin’s deterministic aspects. Bitcoin’s mining infrastructure, difficulty adjustment, and energy constraints introduce physical limitations that shape its behavior. This deterministic framework, grounded in energy consumption and optimization, behaves very much like a physical system. Yet, Bitcoin’s social aspect, often likened to a social network, interacts with its physical infrastructure in ways that create self-regulating feedback loops.

In subsequent work, we used differential equations from network theory (originally applied to social networks like Weibo and the arXiv) to model Bitcoin’s growth.
See here:

https://bitposeidon.com/the-power-law-theory/f/modeling-bitcoin-growth-with-network-theory

These equations, well-established in the study of real-world networks, showed that Bitcoin follows the same kind of power law regularities observed in traditional social networks. It is crucial to highlight that network theory is a recognized branch of physics, with prominent physicists like Albert-László Barabási contributing to our understanding of networks through physics methodologies.

https://www.amazon.com/Linked-New-Science-Networks/dp/0738206679

Moreover, the fields of econophysics and sociophysics have successfully applied physics-based methods to study economic and social systems, further solidifying the idea that social systems can — and often should — be considered physical systems. Social networks and systems, like Bitcoin, consist of many interacting agents. Much like a gas is composed of molecules, the individual free will of agents does not negate the broader physical laws that govern the system’s overall behavior. In fact, social systems are modeled as physical systems using techniques from statistical mechanics, network theory, and information theory — all of which have their roots in physics.

It’s also important to correct the critic’s narrow view of information theory. They treat it as something separate from physics when in reality, information theory is fundamental to physics. Many physical phenomena, including entropy and thermodynamics, are now described through the lens of information theory. This is no different from how Bitcoin’s decentralized ledger or mining difficulty can be explained using both physical and informational principles.

As explained in the Preface, lastly, even if one dismisses the argument that Bitcoin shares similarities with physical systems, it does not invalidate the empirical regularities observed in its price and on-chain metrics. The claim that Bitcoin resembles a physical system is not a prerequisite for recognizing these regularities — it is simply a useful framework to explain why such patterns emerge. Regardless of interpretation, the empirical validity of the Bitcoin Power Law Theory remains undisputed.

Conclusion:

In summary, Morris’ critique is built on misunderstandings of power laws, feedback loops, and scale invariance and an evident lack of familiarity with the vast scientific literature on the topics that the article attempts to discuss with misplaced self-appointed authority. The Bitcoin Power Law Theory has been developed through years of observation and analysis, using rigorous mathematical frameworks that have been applied successfully in a variety of fields, from biology to finance. The evidence for power law behavior in Bitcoin’s ecosystem is overwhelming, and the theory provides a reliable framework for understanding Bitcoin’s long-term trajectory, even in the face of short-term social and political events.

The critique seems aimed at oversimplifying the theory for the sake of attention, without engaging with the actual mathematics and logic behind the model. I hope this response clears up these misunderstandings and reassures readers about the strength and validity of the Bitcoin Power Law Theory.

References

1 Wilde, M. M. (2017). Quantum Information Theory (2nd ed.). Cambridge University Press.

2 West, G. (2017). Scale. Penguin Press.

3 Barabasi, A.-L., & Frangos, J. (2002). Linked: The New Science Of Networks. Perseus Books Group.

4 Ziemann, V. (2021). Physics and Finance (1st ed.). Springer.

5 Galam, S. (2012). Sociophysics: A Physicist’s Modeling of Psycho-political Phenomena (Understanding Complex Systems). Springer.

6 Aoyama, H., Fujiwara, Y., Ikeda, Y., Iyetomi, H., Souma, W., & Yoshikawa, H. (2017). Macro-Econophysics: New Studies on Economic Networks and Synchronization (Physics of Society: Econophysics and Sociophysics). Cambridge University Press.

7 Barabási, A.-L., & Albert, R. (2002). “Statistical Mechanics of Complex Networks”. Reviews of Modern Physics, 74(47), 47–97. https://doi.org/10.1103/RevModPhys.74.47

8 Zang, C., Cui, P., Faloutsos, C., & Zhu, W. (2018). “On Power Law Growth of Social Networks”. IEEE Transactions on Knowledge and Data Engineering, 30(9), 1727–1740. https://doi.org/10.1109/TKDE.2018.2801844

9 Newman, M. E. J. (2003). “The Structure and Function of Complex Networks”. SIAM Review, 45(2), 167–256. https://doi.org/10.1137/S003614450342480

10 Leskovec, J., Kleinberg, J., & Faloutsos, C. (2007). “Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations”. ACM Transactions on Knowledge Discovery from Data (TKDD), 1(1), 2. https://doi.org/10.1145/1217299.1217301

11 Kossinets, G., & Watts, D. J. (2006). “Empirical Analysis of an Evolving Social Network”. Science, 311(5757), 88–90. https://doi.org/10.1126/science.1116869

12 Barabási, A.-L., & Albert, R. (1999). “Emergence of Scaling in Random Networks”. Science, 286(5439), 509–512. https://doi.org/10.1126/science.286.5439.509